 Okay. Good evening everyone and welcome to your sixth session of Accolate. Please make sure that you complete the register in the chat before you leave today and today's session we're going to be discussing amortization and I hope you have your financial calculators but if you don't have your financial calculator it's fine I will show you how to do the questions manually but when we do activities sometimes you might not be able to catch up with us because we only have one hour 30 minutes I will try my level best to accommodate both those with the calculator with the financial calculator and those without a financial calculator it is very important that we do that so that we don't leave anyone behind. So in terms of the session next week will be the last session that we're going to have and I'm assuming we or not assuming I'm planning to do manipulation of equation but I'm going to extend it not just focusing on the just how to solve for x or how to solve for y but includes simultaneous equations include inequalities as well so if those who are doing B and U you might find some of the content not relevant to you and some of the content might be relevant for you but because you're doing B and U the chances are next day you will be doing QMI or next semester you will be doing QMI therefore it means it's easier when you have the knowledge and the skill and it will be something that you not silly for the first time so bear with me on that note because that is our last session in terms of actual academic literacies and then I planned on doing exam preparations because here we've got two modules we're going to split it on the 6th of June only those who are doing B and U you must come to this session I will also share this on the WhatsApp groups as well and then on the 18th of June only those who are doing QMI can also attend that because then the B and U students you will have written your B and U exam as well or a day or also you would have written your exam okay so let's get on to today's session which is amortization before we do that do you have any questions for me before we begin any questions any comments no questions no comments for me then we can start this session like I said we're going to be doing amortization and I expect you have your calculator and you need to also know and understand how to answer the questions without using your calculator as well in terms of using formulas by the end of the session today you should be able to calculate payments of a mortgage or a loan it can be for a car or something so you should be able to calculate payments of a loan and some of the concepts we have lent them the last time if you would watch annuities annuities are payments and we are going to continue and doing the same to calculate the payment we're going to use the annuities but we also going to use the present value of an annuity formula to calculate the payment for amortization once you have your payment then you are able to set up your amortization schedule and in terms of your modules you should be able to answer the questions based on your amortization schedule as well so we're going to teach I'm going to show you how to set up the amortization schedule manually and also I'm going to show you how to set it up using your calculator and remember with the calculator always the steps are the same the first step you do is to clear your calculator from any start beams so we're going to follow the same concepts that we have been doing the whole time okay so what is amortization in general amortization are just all your liabilities both the principal and interest that are paid by a sequential equal payments that are made at an equal interval of time so in your modules QMIO BNU you also need to realize that they will not ask you to change interest rate they will not ask you to change the number of payments while you are working on the problem only the next question might ask you if interest rate have changed and then you can just adjust but you go into your interest and your payments will stay the same for the duration of the period of your amortization in your module okay so in terms of the payment we're going to use the present value of an annuity and that is the formula to calculate don't ask me what this a and i mean because then this is your payment is your principal your present value divided by the accumulation factor of an annuity which is one plus i which is one plus i to the power of n minus one divided by i times one plus i to the power of n and that is your accumulation factor which is this so you must remember the formula for present value of an annuity so as the outstanding principal decreases with your payments the interest you owe at every period will also decrease because the interest we're going to always calculate it using the principal amount as well the fraction of the payment which is available for reducing the principal will increase with the time so it means when you look at your principal value which will be the last column that we work on every time you make a payment that value will always increase with time because that is the value without payment that absolutely without interest that is the amount that you are paying towards your loan excluding interest and it will increase with time then to create an amortization schedule based on all the information that i just explained to you you need to have a period which it can be quarterly yearly by annually in this instance my table shows the year but this is generally your period so how many amortized values you're going to have so if it's quarterly and it's for one year therefore it means you will have periods there will be four of them because it's yearly it's four if it's two years that means you will have eight periods which means those will be the eight times that you will make the payment your first column after the period will be your outstanding principal or your present value or we can call it the outstanding principal or we can call it the closing balance or we can call it the opening balance it will be an opening balance for that year but in the following year it will be a closing balance and also an opening balance for the previous year your b will be your interest we always calculated using the simple interest rate and i will explain more on this later on when we do some activities we always use simple interest remember simple interest is i is equals to p times r times t your payment that will be your present value of an annuity payment that you would have calculated and that is the first thing that you calculate and then the principal repeat it is just your payment minus the interest so what i just explained the first step that you do with amortization schedule is to draw up a table that has the period op which is outstanding principal your interest your payment and principal repeat once you have that table the first step that you do is actually is to calculate the periods you populate your periods depending if it is compounded monthly and for five years that means you will write 60 rows one up to 60 on your amortization schedule that will be your period then the first step that you will do is to calculate the payment once you have calculated the payment then you can calculate your interest by using the simple interest your t will always be equivalent to one or equals to one because it's for that year or that period or that time which will always be equals to one the others might change your p will be your outstanding principal at that point your r will be the rate divided by the compounding periods because it will be compounded so your rate you will have to divide by the compounding period your period team will always be equals to one it doesn't change it will always be one your principal repeat will be your payment the amount you calculated in terms of the payment minus your interest and the other thing that you need to also remember is once you put the periods all 60 of them you also calculate your payment and your payment you completed it stays the same for the entire duration of your loan so if your payment was 200 you go into right here 200 200 up until you get to row number 60 if there was five years compounded 12 uh monthly and so it will be 60 you will write the same 260 times and your outstanding principal will be your previous outstanding principal minus your principal repeat and that will give you your closing balance so for line number one it will be your opening balance will be your present value of the amount that you are loaning so if you take a loan of 250 000 the first row will be 250 000 then you calculate your payment on that 250 000 you calculate the interest and from the payment and the interest you calculate the principal repeat and from the principal repeat we need to create a closing balance in line number two the closing balance will be your opening balance on your first line minus the principal repeat of the first line and that gives you your closing balance but it is also your opening balance for year number two or for the period number two so period number two you go again you calculate the interest based on that period number two because your payment is already there you just calculate the interest on period number two and then calculate the principal repeat by subtracting your payment minus your interest that gives you your principal paid for payment number two once you have payment number two done with the principal repeat you go to line number three you want to create a closing balance by taking the opening balance of line number two subtract the principal repeat of line number two that gives you the closing balance and I know that I am talking like this is like I'm saying something let's do it so that you can see what I am referring to let's draw up an amortization schedule for a loan of 4 000 for three years at 15 per cent per annum compounded half yearly and it is repayable in six half yearly payments the first step of everything that you do is read the statement make sure that you understand what the statement is asking you to do and identify the facts that are given in the statement highlight them write them draw them do whatever you want to do with them but make sure that you understand what is given and if there are any formulas make sure that you write that formula down and use that formula to calculate okay so we now know so we now know what we need to be doing because the statement said we need to draw up an amortization schedule in the exam they will not ask you to draw up an amortization schedule right they will ask you question based on an amortization schedule but you need to know how to develop one or how to draw up one what else are we giving we are told that the loan is of 4 000 that means that means they have given us the present value and they are telling us that it's for three years therefore our period t is three years and what else and they telling us that the rate is 15 so it means our an is 0.15 what else and they say it is compounded half yearly so my compounding period half yearly it means two twice in a year half yearly they're splitting the year into two parts so therefore it is two and since I know what my compounding period that I need to come to my year which is t I must multiply it with the compounding period and I must divide let's use the division sign the the mathematical division I must divide this by two and they say it is repayable in six half year payments so which means there will be six of them because three times two is six okay so I identified everything I need the first step of amortization schedule is to draw up the amortization but now I'm going to first calculate my present value of an annuit I'm given my p I need to calculate r and I have my interest I have my periods then I can just substitute so I've already identified everything I need I can substitute into the formula so like I said previously the i or the r r i interest same t n depending on which one they use in your book um t or n so yeah we're using n so our interest is 0.15 divided by two which is 0.075 0.075 and your n is three times two which is six so we just substitute into the formula and we calculate the period the payment and our payment it's 852 right now let's draw up the amortization because now we have the payment so we go we take the payment that we have we draw up our table and I complete all their periods remember I told you that the first step you do is draw up write the period the present value of the first one or the outstanding principle of the first one will be the present value that was given so there I write it down the next step is for me to complete the entire table with the payments because we did calculate the payment and I just calculate the payments or complete the payment and I calculate the total of those payments therefore it means I'm going to be making or uh five thousand one one three point zero eight payments okay for six years for the two years that or three years that we have because then those will be the payments okay now the next step is to calculate the interest that's the second one so our interest remember we use our interest we use the present value times the rate times the periods so it's four thousand times our rate is zero comma zero seven five times one always remember it will be t will be equals to one all their time and that will give us so the first thing we calculate is the interest so those are the formulas that are going to be using so we say four thousand times zero comma zero seven five times one oh come on I don't want to forget the whole table as yet and that should be equals to if you have a calculator I think it's 300 is my calculator not do you do do do what is the answer 300 is 300 right so we're going to write it here that will be 300 now to calculate the principal repeat we say 85218 minus 300 which will be equals to five five two point one eight that will be the answer five eight hundred and fifty two point one eight minus 300 will give us five hundred and fifty two point one eight now to get to the outstanding principal or the closing balance here we say four thousand minus so we say outstanding principal minus the principal repeat four thousand minus five five two point one eight we say four thousand minus five five two point one eight and it gives us three four four seven point eight two we need to go back and calculate the interest so calculating the interest yeah instead of using four thousand now we use three four four four seven point eight two and therefore we're going to get times point zero seven five times one and that gives us three five eight point five nine point five nine and to calculate the principal repeat we say eight five two minus two five minus two five eight point five nine and we get the principal repeat of five nine three point five nine and to get there for the for the next one we do the same three four four seven point eight two minus five nine three point five nine we write the answer there we calculate the interest and you can continue and continue and continue to complete the entire table and you will have all your various completed and you can add all your interest they will give you the total interest amount you paid for the duration of the period for those six half years and you will have the total in terms of your principal repeat which is the same the total should be the same as your opening balance at the beginning or it should be the same as your present value if you don't get the same when you add all of them then it means that you are doing something wrong okay so that is your amortization schedule what can you do with this amortization schedule so they will ask you a lot of questions for example they might ask you what is the payment or not the payment what is the interest amount you would pay after making three payments after i make three payments the interest that i would have paid would be that amount or they can ask you what is the closing balance after four payments after i make the four payments which is at that point what will be my closing balance because i made this payment my closing balance will be 1500 entage remember that so your closing balance will be the opening balance of the next line so after four payments because that will be my fourth payment my closing balance will be 1500 entage if they ask you what is your opening balance when you make four payments then your opening balance is 2260 so you can use this to answer the questions they might ask you what is the total amount of payment that you would have paid or what is the total interest you would have paid your total interest will be 1118 otherwise you can calculate your total interest so your total interest can also be your sum of all the payments which is 5113.08 minus your principal amount which is your principal value and that should also give you 11 113.08 that's all what they can ask you what is the total payments that you would have made or what is the future payment future value of this amortization amortized value then your future value will be 5000 113 that is if you're going to be calculating manual but that does not mean those with the financial calculators you cannot also understand this because sometimes i'm going to do that example yeah sometimes they can give you an amortization schedule and they might have blocked out this value and they call this value a and they might have blocked out this value sorry i can't see your screen i'm not sure what's going on i also don't know what went on and the screen is off when when was the screen off when you were trying to finish up on the on the last total interest on the total interest yes we are calculating the total interest oh okay and then the screen went blank oh sorry about that we can also catch up on it later on so i'm saying also if they give you an amortization schedule and they blank blanked out all these values and they say this is a and this is b you should be able to answer this question because you cannot answer a if you didn't answer b or let's say also this is blanked out let's assume that this is also blanked out because you can answer a even if you don't have b so let's say all these are blank out and they say it is a b c so in order for you to calculate b sorry a you need to calculate c in order for you to answer c you need to answer b so to answer b you need to know that it is your b b is p r t which will be 2216.12 multiplied by 0.075 multiplied by one that should give you the value of b which is 166.21 in order to answer a we need to answer b c and we know what c is c is 852.18 minus 166.21 and that will give you the answer that you are looking for which is 685.97 and then you can answer a and your a will be 2216.12 minus 685.97 and that should give you the answer of 153015 so regardless of whether you have a financial calculator you need to be able to know how to complete the amortization schedule finish in class let's move on to those with a financial calculator and see how we can help them to do the same oh this is what I was explaining right now but how do we do amortization schedule when we're using a financial calculator same question same same same the first needs to clear our calculator from any stored value so we need to also identify what it's given here so we are asked to draw up an amortization schedule so on a piece of paper you can draw up your table we know that this is our present value that is pv we know that this is our n we know that this is our i slash y and we know that it is compounded p slash y it is compounded of a which is 2 the first step that we need to do is to clear our calculator from any stored values and calculate the present value plus or minus also we do a second function p slash y we press 2 we go ent and that is your compounding period then you go on and off your calculator then we go plus or minus present value of 4000 which is our pv I forgot on this slide to have my pv that is your pv then we put three second function times p slash y which is three second function n and again and that is when we store the periods and we go 15 i and y to store the interest and we compute pmt so c o m p pmt and once we have our payment then we can amortize this value on your screen you will have your payment of 852.18 which is the same as what we had previously and you can draw up the schedule and you complete everything that everyone from the manual calculations also did we complete that and then we go and start to amortize the payment completing the table then we're going to amortize the payment to amortize your payment you press amort and press 1 so you will press a mrt and then press 1 to say I am now amortizing my first payment then you press down arrow and then press 1 and say I am confirming that I am amortizing my first payment and then you press enter and you press down arrow it should give you the balance which is your closing balance after payment number one which will be your opening balance line number two and payment number two the answer will be in the negative don't worry about the negative in front so you will just write 3447.82 and then you go press the down arrow it will give you the principal amount which will be the last color on your amortization schedule and then press the down arrow it will give you the interest so on your calculator it works different tool when you are calculating manual remember when we calculate in manual the first thing we do is calculating the payment which is similar then we calculate the interest here it gives you the balance before interest so do interest principal and then the balance so on your calculator it does things in reverse it goes interest principal it goes balance principal interest and then you press down arrow and now we want to amortize the second payment you press down arrow to enter down arrow to enter so you need to repeat the steps twice so that the first one says I am doing this the second one will say I am I am confirming that I am amortizing my second payment and then you will do the same repeat the steps so many times so you will press your down arrow and it will give you the balance of 285 down arrow it will give you your principal which will give you the principal of the first the second line down arrow it will give you the interest of the second line and you go down arrow three enter down arrow three enter and we are amortizing the third payment and it will give you your closing balance principal repeat of the third payment interest of the third payment and you continue like that down arrow down arrow down arrow until you are at the end and that's how easy it is to do amortization schedule on your calculator now let's look at what if they are asking you to do this on your calculator the same thing that we did with the previous one so you are using your financial calculator right you are giving the statement which looks like this that says draw up an amortization schedule of these but they asking you what is the payment what is the principal balance after five payments uh after four payments right what is the outstanding principal after four payments the first thing you need to do in everything is to calculate your payments first so you will go and follow the step second function c a second function p and y to e and t on and off your calculator plus or minus you put in the four thousand uh and you say it's the present value you go 15 which is i and y three second function and and again which is the period and then you say comp pmt and it gives you the payment and then you go and press amort so you will start with the amort nicely and then you say one remember we're looking for op after four payments right so we say amort one down arrow one e and t and without even looking at the values you just press down arrow down arrow down arrow once it gets to interest on your down arrow then you press down arrow instead of going to two you don't do two you say four e and t and you say down arrow four e and t and you go down arrow it will give you the answer you are looking for those who are calculating manually they have to do the whole table up until they get to four in order for them to get to a so they will have to complete all these values all of them all of them before they get to four on your financial calculator you do not have to you need to calculate your payment you calculate your first amortization your first payment you need to amortize your first payment before you can answer any of the other questions and if they asked you what is the what is the payment no the interest what will be the interest that you would have paid after four payments and that will be seen so you will just press down arrow and then down arrow again and that will give you your pay your interest remember this is your principal repeat and the next one will be your payment your interest and if they ask you what is their total payments you have your payment you can just add them all up or you can go back and put um if they ask you what is your total payment on your calculator you have your payment so you can go and say uh comp again you can go back to comp and say p m t again and it will give you the payment and then multiply that payment by six and that will give you six uh five one one three if they say what is your total interest that you cannot do unless if you have the entire schedule but you can calculate what your total interest is because if you calculated your total payments which will be five thousand you can just subtract four thousand and that will give you your total payment easy easy easy easy easy easy so let's look at more exercises do you have any question before we move to the exercises hi Lizzie yes yes um i wanted to find out quickly before we do when using the calculator before we we can do anything do we uh calculate the payment that's the first thing when we work with amortization you will realize as well when you answer your assignment questions or your exam questions the first question that they will ask you on amortization will be payment we'll look at that some of the examples how the questions follow each other okay and what you need to look up for so but the first thing that they will ask you when you're doing amortization is calculate or how um what will be the payment the minimum payment or the amount of payments that they need to make that is your um your your first question then the second question might ask you what is the outstanding balance after five years that's the other thing that is very tricky with the questions so for example if they say what is the payment after two years remember there it said three years if they say two years this is not two years that is still one year remember a year is made up of two halves so two payments will be done in one year so you need to be aware of that that this is three years because we're making two payments every year so if they ask you what is the outstanding principal after two years not for payments after two years after two years what is the opening principal after two years which is the same as after payment number four right so you need to be aware of those scenarios when they ask you questions like that so let's look at examples let's go and look at more exercises so here we can work together those with a calculator and those without a calculator we need to be on the same page to see are there any questions on the chat is there anyone who's asking a question no questions please make sure that you complete the register i'm just going to post it again on the chat before you leave today make sure that you have completed that register okay so let's go to our exercise a farmer needs 250 000 to purchase a 10 ton trailer the bank approves the loan for the full amount the interest rate is 18 percent per annum or per year compounded monthly and the loan has to be paid off in five years time determine the farmer's minimum monthly salary so this might be question number 22 on your exam usually amortization are your last questions in the on the exam paper so this is question number 22 so it means question 23 24 and 25 might be related to the same statement that we are reading so the first question asked determine the farmer's minimum monthly payment so what are we given the present value so we're going to start with those who have late in manual right present value which is p and we know that the bank approves all the full amount so its p is 250 our interest i is 0 comma 18 and we know that it is compounded monthly what is compounded monthly how many there will be 12 compounding periods there will be 12 so it means our interest we will have to go and divide it by 12 and the loan has to be paid in five years time so which is our n which will be five times 12 therefore it is 60 and what is 0 comma 18 divide 0 comma 18 point 18 divide by 12 divide by 12 which is 0 comma 0 0 comma 0 1 5 that is our interest so those who are calculating manually then you will use your formula i'm not going to write the actual formula as it appears but i'm going to write the formula s r is equals to your p divide by the accumulation factor so that it's easy for you to substitute into that formula 1 plus i to the power n minus 1 divide by i times 1 plus i to the power n so we just substitute into this formula our principal or present value is 2 500 000 divide by everything in the accumulation factor will be 1 plus 0.015 to the power 60 minus 1 divide by 0 comma 015 times 1 plus 0 comma 015 to the power 60 and you can calculate and give me the answer later on those who are using financial calculator we do the same remember the steps are always the same i'm gonna change or not let me not change the the test i'm going to use the same pen so remember the steps are the same present value is our pv interest is our i slash y compounding periods they are 12 and n is five remember we keep the values as they are and n is five we don't multiply by 12 so you go second function ca second function p slash y which is on top of i and y put in the compounding periods and then press ent go on and off your calculator plus or minus put in the value of the present value and and then press present value then we go what is the value of our interest put it in the right place what is the value of our period second function and you know me i'm lazy to type i'm just gonna press n n again so you press n twice in this instance which is times p y which we multiply with the compounding periods and then we're going to say c o m p p m t so are you done let's do the calculations then you can give me the answer when you are done okay you must write your answer in the chat and if everyone agrees with your answer you know what we do usually we like we thumb i what do you call that thumb what thumb like we live it we laugh at it or we are surprised by it or we are sad but we never become angry so you can use any of those emojis like love like love love heart heart it laugh at it i'm not sure even laughing at it will be a good idea surprised by it sad by it but never angry so if you agree with mildreds let's see how many people we've got about 20 got about 24 people on here so they should be at least different answers different emojis if possible give us what you have in front of you hi bo something is weird somebody's answering with my name and i haven't answered who is you who's answering with your name mildred m it's me but the person is already no they are coming threads sorry there is oh mildred antebola is the one who's answering and then we have uh qmi guest huh that's very nice we have a guest so come come come come so we have i'm gonna say seven half we are not even half of the people who are here i want everyone to give their opinion on the answer so i'm gonna take it some of you don't know how to answer it because if you are not liking the answer or commenting or giving us your own answer it means you haven't calculated it so it's fine let's answer the question so what is those who are who calculated manual probably you had the same answer as those who calculated using a financial calculator so those who use the financial calculator i'm gonna ask you first what are the values that i need to put in the blocks to see that you did the right thing so second function py what was the value that you put in here okay plus or minus 250 000 and i and y 18 and your periods that will be five and when you press c o m p p m t and the answer will be equals to option four six thousand three hundred and forty eight and once you have that answer you don't remove anything from your calculator you hold on you don't delete you don't do anything you just leave the answer as is and look at it those who are calculating manually you would also have gotten the answer of six thousand three hundred and forty eight point three six now you will have to do some work because you don't have all the answers the second question says refers to farmer's question number one which means in your exam paper you are referring to question number 22 so now you are in question number 23 it says refers to question number 22 what will the outstanding balance of the farmer's loan be at the end of third year right third yeah those with financial calculator it will be easy i'm going to come back to you those without financial calculators therefore it means you will have to go and draw up an amortization schedule somewhere either in excel or somewhere so you will have your period your opening balance your interest i'm just going to put the i for interest not i i i is for interest and p m t for payment and pr for principal repage right you go in to say because the let's go back to our question number 22 so question 22 was 60 right and it's monthly so one two three four five six seven eight nine ten up until 60 your payment you calculated it and it was 6348 6348 point what was the point 36 and your opening balance was 250 000 right you need to calculate your interest by saying 250 times what was our interest 0 comma 015 so to calculate this value you will say 250 000 times 0 comma 015 times 1 it should give you your interest here to calculate this value here you will say 648 minus the let's make it the question mark to calculate the question mark so this is to calculate the point right to calculate the question mark you will say p m t minus the point which is that that answer that you have there and you will have to do the same so let's go to this one i will make it the block to calculate the block to calculate the block you will say 250 000 minus the question mark and that will give you your thing and then you go back calculate the point by using the value there by calculating there because this payment will stay the same for all the years to calculate the question mark and then calculate this and until you get to the third year you know where is the third year it's monthly so there should be 12 rows of this and you should also have calculated another 12 rows because this is year one year two and the third year will be after 12 36 so somewhere here there will be 36 that will be the last that you are calculating 36 what is the outstanding balance on the farmer's loan at the end of third year year one is made up of 12 months year two is made up of 12 months year three is made up of 12 months so at the end of year three which is the third year will be at the end of 36 so you will have to complete this 36 times in order to get the video now right i'm done with you so because you've got all the time until the session is over to complete the amortization schedule so it means in the exam you will not be able to answer that question as quickly as possible so those with a financial calculator here is the thing you will say second function c or you have already the amortized the the value we need to amortize the payment so you still have your payment if you remove your payment just go back and say comp p empty and your payment should still appear on your calculate once you have that payment then you press amort a m r t you press one press down arrow down a you press amort one and you press down arrow one and then you press e and t then you're going to press down arrow down arrow you're going to press it twice three times because the first one it will give you the balance the principal repeat and it will give you your interest and you will get to down arrow now it says at the end of the third year three times 12 is 36 at the end of third year it's after 36 payments so you're going to press down arrow 36 e and t then arrow 36 e and t down arrow and it will say the balance and that is the answer we are looking for and what do we have let's see how many answers no answer no answer i got option three hundred and twenty seven so the answer will be hundred and twenty seven thousand one hundred and sixty point one six those who are using the manual calculator on the notes i'm going to stop sharing now i'm gonna stop sharing so that i can share my entire screen oh gosh now people are gonna see my whatsapp let me close my entire screen people are going to see because this is published i'm looking for so those i'm just gonna show you those who are calculating manually you just go to the scheduled link you go to open class folders there is a i've just placed the amortization hack thingy there which you can use so but you will have to change certain things on here enable you to use this as your calculator so i've just made it so let's go and see if i can get it to work the way it's supposed to interest is 18 and the number of years here you need to be very careful because i'm using already the compounded possibly let me just see the number of years if it's five and the compounding periods if they are 12 just want to see if i'm getting it right so you will have to use it that way and i'm just explaining that these three things are just calculations so the payment what i do here it is just this formula that i've calculated the top part of the formula calculates that the bottom part of the formula is this complex calculation that is happening there at the bottom can you see that um that's all what i'm doing but you can see that the payment you get the same as what you have when you calculate manually and the amortization schedule is completed now the challenge with this is it will not give you up until where you want because then there will be some other things that happens here at the bottom i've done it up to 60 so you can also fix it because it's just calculations on how you go and amend each one of them so i just did it up to 60 but after so it will give you the same answer so after 36 months or after 36 payments so you just go to 36 to 36 and we know that this is the 36 payment but what we're looking for it is the closing balance after we make this payment after we make 36 payment this is our 36 payment that will be our closing balance as you can see it answers the question that you were asked which is option number three okay so i've given you everything you need for now let's go and answer number three so 22 23 24 now we are at 24 and question 24 it says also refer back to the same question that you had previously now they're asking you how long will it take to pay off the loan if the farmer pays 7500 monthly into the account assuming that the interest stays the same now you panic don't panic because now they're asking you for the period how long will it take them we know what the loan is you know what the payment is right so we do have the payment we do have the present value we do have the interest we just don't know how long which is end we have the interest and we don't know the end so we don't panic only those who are going to calculate this manually might panic because you will have to use the formula and change so yeah you will say second function see sorry that's the other thing i need to say you don't have to change anything everything stays the same right on your question so because they are related the compounding periods are the same everything stays the same now the only thing that changes is the payment your present value still stays the same so you're going to press 7500 and then you're going to press PMT on your calculator these are financial calculate so you haven't cleared your calculator from anything after you calculated the previous question you still have all the values so you just press 7500 and you press PMT and then you go and press comp and you press end and when you press n it should give you a value in a compounded number so tell me what you see in front of you now i'm talking to those who are calculating using their financial calculator what is the value that you see don't look at the answers we're going to get there what value do you see if you cleared your calculator let me know that i've cleared my calculator then i will give you the steps in the meantime no i've also cleared my calculator okay so if you cleared your calculator still the same second function CA so we do the same second function CA second function p slash y and you press the 12 when you do ENT then you go on and off your calculator plus or minus one of them seven seven thousand five hundred or the two hundred and fifty thousand present value seven thousand five hundred PMT and our interest was 18 which is in y and you say comp and you press n those who are calculating manually gosh that is the very complex thing to do so our present value times our rate times one plus i to the power n minus one divide by n times one plus i to the power n now your challenge will be how do you use the log so now you will need to rewrite this which might not be as easy as i thought so let's see it will be p divided by r and you will have your one plus your i to the power n minus one divide by i times one plus i divide by n you will have to substitute the value so that you can you will need to make and the subject of the formula i will show you just now if we have time how to do that but i want those who are calculating yet to give me the answer what is the answer when you do this when you press comp and give me the value that you see in front of don't look at the answers because then you go in to say but i'm not getting the same answer that i'm seeing here don't worry about the answer that is on the board on the screen use me the answer that we see on your calculator 36.5 46.5 46.5 right so the answer you get is 46.5 now this says how long it they will take the to take to pay off the load but the answers on here are in years the answer you see here is the compounded answer of your periods already this answer is multiplied by the compounding periods all you need to do is divide this by the number of compounding periods we know that they were 12 because that's what we put there they were 12 so you just say 46.5 divide by 12 and then you will get the answer so you just need to pay attention to that so it is 3.9 so that is the answer you just need to make sure that you pay attention to the option given are they giving it to you in months because if it's compounded monthly it should be in months if it's compounded quarterly if they give you in quarters then you know that it is in quarters the answer you get will be in quarters but if it's in years then you need to make sure that you divide the answer you get for n divided by the compounding periods and this happens when you do any questions relating to compounded interest annuities and amortization every question where they ask you to find the value of n or the how long you answer the question of how long always remember if it was compounded only for yearly if it's compounded yearly therefore the answer you get is in years then the answer will be in years so you just need to check if there are no disconnection between the two those who are calculating manually you need to make sure that n is your subject of the formula and that might take long because at the end of the day you will have to use the log to manipulate this entire equation so that n is the log n is the subject of the formula so it means you will have to use the logarithm function okay that is the only question that you might it might take you long if if not you might not calculate it in the example if you are going to sacrifice at least one question that you are not going to answer but in terms of amortization the others should be fine because you have the table okay so this is another example I just want to check what type is it because we left with seven minutes so this is another example of amortization now you need to pay attention guys when you get closer to the end of your your exam paper especially the last three or four questions of the exam paper they are about amortization therefore all those questions are related to one another don't be quick to clear your calculator before you finish your exam and question that is related to amortization there will be three or four questions related to that make sure that when you move to the next question it's not related to that question before you clear your calculator pay attention to that so exercise four it says Justin here bought the three house bedroom for 480 he paid the deposit of 150 so therefore it means the amount now reduced and he secured the loan for the outstanding amount the yearly interest rate on the loan at that stage was 24 percent and it was compounded monthly and the time of the loan was 20 years determined just in minimum payment so we know that our present value will be 480 000 minus 150 000 that will be your present value we know that our interest will be 0 comma 24 and you need to divide that by the compounding periods they are 12 the year or periods they are 20 and you will need to multiply that by 12 so let's go to our sheet so that we can complete this oh it closed okay i can go and open it again they didn't realize that i closed it oh i didn't close it still yet so we're gonna go i'm gonna use the same so i'm gonna say it's 480 000 because i can then minus and now it means it changes your your sheet because i'm working on online 480 minus 150 000 let's see if this is 450 yes and we know that our interest was 24 and the number of years they were 20 and it is compounded monthly which is 12 so this i have my compounding period and i've calculated my payment is 660 6657 let's see and that is option number one easy net otherwise you go and do second function c a second function p slash y they are 12 e and t on and off your calculator plus or minus 330 000 that is our present value we go and put 20 second function and and again and 24 that is my interest and i go comp and that will be comp p m t and that will give me my payment now i need to answer the second question i don't clear my calculator go to the next question and it says relating to the previous question determine the outstanding amount at the end of 10 years 10 years compounded monthly how many payments will that be so you just need to say 10 times 12 and that should give you your your next payment so how many are they 120 payments unfortunately oh unfortunately on our sheet remember our sheet does not have 120 so you will have to work on that sheet because it ends on 260 and not up until 120 so i can just continue i'm not sure if i can add more columns on this but since it's online i don't know how to do that online okay let's see if if it was still work still works so you will have to add more columns insert rows can insert as many as i want and then i can drag this so that the number here gets 220 because that's what i need still i'm still on 115 so i must still add more insert and you just go to the top three because i need to keep the same calculations and formulas and you just drag and my 120 there it is so what is the balance after 120 so that is 120 that is my payment at 120 therefore this is my answer that i'm looking for which is 301951 which is option number three and that's how easy it is otherwise those who are using financial calculator after you have your payment remember you did the comp pmt you wait there and you just say amrt1 and then you go down arrow 1 ent down arrow down arrow you just even ignore all that because until you get to interest there you go down arrow and you press 120 ent down arrow 120 ent and down arrow and it will show you balance and that is the answer that you are looking for that's how easy it is to do amortization the next question also it relates to the same so please don't clear your calculators you have your payments all you just need to do you read the question it says suppose he has to pay 8 000 per month into the loan account from the start how long will it take we still back to that how long so everything stays the same how long if i change you just press 8 000 and you press pmt it will overwrite the original payment that you have and then you just press comp n and it is in years you divide that by the compounding periods and you can get your answer straightforward if you cleared your calculator if you cleared your calculator then you're going to use second function ea second function p slash y 12 ent on and off your calculator plus or minus now i'm gonna put the 8 000 because it doesn't really matter any one of them can have a plus or minus but only one of them plus or minus 8 000 and 330 000 that is our present value and our interest was 24 and that was i and y and we just need to comp and and when you get that we divide it by 12 what is the answer and that will continue today's session have you calculated the answer i'm still calculating okay so those those who are calculating manually i'm gonna show you now so remember this is the formula so what i can ask you to do is copy this formula only the formula not not the equal side copy that paste it somewhere and please download don't do anything to this you must download it onto your machine right because if you make any changes to this sheet you're changing it for everyone so don't work online so you copy it and you paste it somewhere and then you come in here and you type 8 000 and you press equal and it will change everything and probably it will tell you when you will have paid everything up let's see when we get a 0 there 89 so you take 89 and you divide or is it 90 it might be 90 not 89 89 divide by 2 so let's see equals 89 divide by 12 7.4 so it is 90 actually sorry let's see 90 because i haven't calculated it i'm just no which one will be the last one is it 89 or 88 when you use your calculator what do you get i think it's 88 probably you do get 88 what do you get just 88.02 88.02 right and if you divide 88.02 by by 12 you should have 7.3 which is the answer that i get there because there's no payment here it will actually end on there on 88 because this is negative on this side so that will be 88 so you just go and look at the last way before you get to the negative but probably you need to use your calculators and that concludes today's session because then i am way out over type this is another question that you might get in the exam that looks like this and it says first uh find the size of the three monthly payment then consider amortizing the that payment and find the total interest yeah it's very interesting it says find the total interest charged over the first year of repayments reading the question you should be able to it says quarterly so there will be four payments made per year and this is for how long so there will be just only four payments made so you can calculate those and calculate the interest charged over those four first year repayments because they are just four so you can do that you can calculate them okay and that concludes today's session which the next session i see you will be on the day tf i hope you have enjoyed the session and and good luck with all your work so let's just recap and finish off the session for today uh by the end of the session you have learned how to calculate the payment of an annual of an amortization note and you have you now know how to to set up an amortization schedule you need to practice guys practice practice practice practice practice you cannot just come yet today and then wait until you go write the exam and then start practicing a day before you go write the exam using your financial calculator requires you to practice finding more questions and doing the exercise if you are stuck or you don't know what is happening feel free to send an email feel free to ask on whatsapp i might not be the only person you can rely on there are so many other people out there giving assistance in terms of qmi you can ask them don't wait until it's too late and start painting ask go through the work this is meds we need to practice the more you practice the more you get better edit don't be shy okay so conclusion are there any questions any comments are you still good are you happy talk to me before we end the session those who haven't completed the register please make sure that you complete the register yes build that my tabula since there are two build rates in this room i know we yes we we we received a number of session so far i might say this was a tricky one this amortization but uh with your assistance uh at least now we can say that i will be able to answer it uh yeah the only thing i can say thank you for your sessions uh helping me a lot thank you thank you no problem uh build that my table you have your hand up i thought you went to ask your question okay good evening everyone evening i just want to know where can i access this okay so um i don't know how you accessed the session for today i'm gonna go back to the thing here to share i just need to this discount that um i don't know how you accessed the session for today but there is a schedule that unisa paro shares with the students if you go to that schedule and you look for your for this topic which is basic numeracy skills and you look for my name but you might find me in different places you just need to make sure that it's linked to your module there is the join session where you join all the sessions and then underneath it there is the notes and recordings that's why i went to show you where to open the notes the notes are under that if you click on it it will open the notes for you i've got all the notes for all the sessions that we have and underneath the open notes and class open class notes folder there is the recorded sessions they they are all of except there is one missing i've just realized that so this is where you will find the recording it will be loaded here but it takes time it takes about they said is it 62 hours to 72 hours i can't even remember but it takes time uh to get the the the recordings loaded and that is reasonable because there are so many other sessions that are happening on the same day as you can see there they are about one two three four five six more sessions that were happening today so they will need to make sure that they download them clean them up upload them then share them on this site so it takes time all right i'm gonna stop presenting and stop sharing and i can say to you guys thank you for coming and i will see you on the 30th okay so the other thing wait let me check what is the recording stop