 or are you doing both? I'm doing QMI. You're doing QMI, so then you will be here for the rest of the session for today. Okay, so welcome to your fifth session of basic numeracy skills. Yeah, so today's session, we're going to deal with a compound interest. And we're also going to include with compounding interest, or compound interest, we're going to also include how we calculate or answer questions related to type value of your money. So today is the ninth, we're doing compound interest and we look at how to calculate compound interest for future value and present value. Next week, Monday, and I'm so surprised that still on the WhatsApp group, people are still asking, do we have a class today? These classes happens every day, except if it's a public holiday and I have a consent from you to say we can continue. And the classes happens every Monday. Then next week, we're going to look at how we calculate payments or annuities. And then the last one, on the 23rd, we're going to look at amortization and then we go back to the basics, how to manipulate an equation. I might change this from how to manipulate the equations, depending on how many people attend on what. If there are more BNU students, then we will stick to this. But if there are more QMI students, like today is only the two of you, if next week is still the two of you, then we will stick with some type of a QMI type of difficult questions. Like, for example, in state of doing only manipulating of an equation, we might focus on quadratic equations, simultaneous equations, things like that. Okay, because some of these things we covered them in the first session that we had. Do you have any question, comments, query before we start? I'm going to post also the link to the register. Please make sure that you complete the register. If I can find that, complete the register before we start. Do you have any question or comments? If there are no questions, then let's go on and look at how do we answer questions relating to compound interest. By the end of the session today, you need to learn how to do basic calculations looking at compound interest and also at time value of your money. A compound interest is interest paid on interest. The last time we met, we discussed simple interest, which is interest paid at the beginning. This one is interest paid on top of interest. When you borrow money at the bank, and the bank tells you that your amount will be charged interest compounded monthly, it means every month you're going to be paying interest. Because you borrowed money, interest every month will be added, but it means every month you will be paying interest on top of that interest because the interest will be added every month to the amount that you are owing. If you are saving, that will be a good thing because the amount that you are saving every month will accumulate interest that gets paid into the same interest that you already have paid, or you have already accumulated. When we calculate compound interest, we use the formula S is equals to P times 1 plus RT, R to the power of T. You need to have your financial calculator. It's very easy to use your financial calculator than to use the formulas. But if you don't have a financial calculator, you can still use this formulas, where S will represent your accumulated amount, P represent your present value, or your principal amount, and R will represent your interest, your interest rate, which is compounded, and your T will represent the period, which is also compounded. So what do I mean by that? On this formula, when you see or you look at it, there are certain things that you need to be aware of. Your interest needs to be compounded, so it means it will have to be divided by the compounding period, and your time of how long you are saving or how long the loan will be needs to also be compounded. So you need to multiply by the compounding period, and that is how the equation will look. Otherwise, then do the calculation outside and come back and substitute them into the formula. Okay, what are compounding periods? And they can differ depending on what the question is asking you. So you need to always be mindful of the compounding period. When the period or the state that it is compounded daily, you need to know that a day, there are 365 days in a calendar. So daily or day, it's 365, we do not take into consideration the leap year. If it's compounded weekly, there are 52 weeks of the calendar, so therefore it means there will be 52 compounding periods. Monthly, it's 12 quarterly or what we call three months. If the question says it is compounded three months or the payment is made three months or quarterly, so therefore you know that it is equivalent to four because a year can be divided into four quarters. Six months or by annually or half yearly, they mean two because a year can be divided into two. Sometimes they might give you any, none of this. Also, let's complete this table and yearly or annually, it will mean one year, which is equivalent to one. So sometimes the compounding periods, they can say it is compounded four months, using the compounding periods or four months, not monthly, months, that should be an A and S. If the periods, they say it's four months, how many months will make up a year? There will be three, so therefore it means your compounding periods will be equivalent to three because if I take my calendar of one, two, three, four, five, six, seven, eight, nine, 10, 11, 12, and if I split this calendar, full calendar year, into four parts, therefore it means grouping all my months into four months, then there will be three of them. So that is what we call by compounding. If it's daily, then it means I'm going to count how many days, so remember this a week. This is a month, a month has days, days, day two or day one, depending on the month. And if it's a week, a month has four weeks within a month, sorry, within a week, and that will multiply by 12, that will be 52 as well and things like that, so you just need to know how to break down a calendar month into compounding periods as well, depending on how they give you the information. Okay, that is compounding periods. So like I said, in terms of the formula, we say we use P times one plus R divided by the compounding periods to the power T times the compounding periods. How do we do that? So in terms of the compounding periods, we just divide your interest. If they told us that the interest was 12%, which is 0,12, remember 12% divided by 100 will be 0,2, 0,12, and if they say monthly, you're going to divide 0,12 with 12 months. In the periods, if they say it's two years, we take two years, T is our T, and we're going to multiply it by the compounding periods and our compounding periods monthly is 12 and you can do with the rest of the other compounding periods. Like by annually, the interest of 12% will be 0,12 divided by two, which will be 0,06, which will be paid every quarter or every bi-yearly into your account and the number of periods because it's by annually, therefore, how many? Yes, if it's two years, then before it means it will be paid four times into your account. And that's how we break down the compounding periods if we are given the interest and the number of years. So let's look at an example. Now, I told you in the beginning, you need to have a financial calculator, a sharp EL3738 to do this, but you can still also use your formulas. So calculate the compounded amount of 500 invested for 10 years at 7.5% per annum compounded annually. Now remember, with everything, we need to understand what the question is asking. Calculate the compounded amount. So therefore it means we need to calculate the accumulated amount because it's a compounded amount. So that is our future value, which will be our accumulated amount, yes. On a 500 that is invested, so that will be our present value that we are investing for 10 years, that will be our period at 7.5, that will be our rate of zero comma. Remember, 7.5 is the same, oh, sorry, 7.5 is the same as 7.5 because a half is the same a half, it's equivalent to 0.5. So 0.5 plus seven is 7.5. And since it's 7.5 and it's in percentage, and then I can just divide this by 100, therefore it will be 0.775, that is our rate. And they also tell us that it is compounded annually, therefore my compounding periods will be equals to one. That is what the question, what we are given in the question. So we need to first identify the formula. So we know what the formula is. The future value is equals to principal amount times one plus R times to the power of T. We are told what P is. P is 500 times one plus our rate of zero comma. 0.75, but remember we need to divide by the compounding period. And our T is 10 times our compounding periods. And we just substitute the values and calculate. First we calculate what is inside the brackets first. Remember both must rule, what is inside the bracket. 0.75 divided by one is the same as 0.075 plus one. It will be 1.075. 10 times one is 10. So we have 500 times 1.075 to the power of 10. And simplifying the power first, 1.075 to the power of 10 gives us 2.06103 multiplied by 500. And the answer we get is 1,030.52. That's how easy it is to use a formula. But if you have a financial calculator, it is even way better than the formula. We're going to do the same. So on your financial calculator, we should look like this. We're going to use the second function, we're going to use an on and off, we're going to use the mode. Those are the most important buttons that we're going to be using. Can you just give me a minute to go to the other room to get my calculator? Okay. Okay. Okay, got it. Thank you. No problem. Okay. So we're going to use all those three buttons there at the top. We also going to be using this button here, that button there. Actually, I must not even... Okay, we can do that. We're going to use those two and we're going to use that plus that button. So those are for today. Those are very important plus also the numbers. I'm not going to highlight the numbers, but in terms of the functions that we're going to be using today, those are the most important functions. So how do you then are going to work with this? It's going to be very easy and very quick for you to use your calculator, but I want you to get to a habit of not jumping straight onto your calculator and calculating. You will see how I do mine, and then I expect you for every question that you're going to be answering. Please, like those who are calculating manually without a financial calculator, they would write step by step when they are answering the question. I expect you to also write step by step on a piece of a paper or a book that you have the steps that you're going to follow and then use your calculator to follow exactly the steps that you wrote down. And the steps stays the same all the time. And the more you practice, the more you write them, the more you will notice that you don't even need to remember the steps because they will come to you just like that. But for practice papers, I want you to do as I do write the steps down before you start calculating. So I know I've got my calculator it's here next to me, and I need to answer the same question as if I had a manual calculator or a scientific calculator. Calculate the compounded amount of 500 invested for 10 years at 7.5% per annum compounded annual. Now you now need to write this in terms in relation to your calculator. Remember with the formula we use the S, the P and all that. So that will be your second function. That is the mode that we're going to use to clear our calculator. That is the on and off button when I talk about on and off. This is the period when I say second function and again, you're going to press that N. And you will notice that I always I'm always going to say N and N again. It means you need to press the N button twice because when you press second function, we're calling the value that is written in orange there. But I don't have to repeat that value again and again and again and again. I can just repeat the button that you're going to be pressing. And I know why which will be your interest. And at the top of I and why there is a value that is written in orange. That is the first thing that we do on the calculator is to put in the compounding periods. So I and why we're going to press it so many times as well. But when I say second function, I and why that is the first step that you do on your calculator all the time before you press the on and off button. Then we also have the present value and the future value. I forgot about the main the main button. The C O M P which is compute. The comp button is to compute whether we want to compute the future value or whether we want to compute the present value or whether we want to compute the interest or whether we want to compute the whether we want to compute the periods. Whether we want to compute the periods. Whether we want to compute the periods. Okay. And then the E and T we're going to use it with the compounding periods as well. Okay. So now let's find out what we are giving always identify what you are asked and what you need in terms of the question. So the question says we need to calculate the compounded amount which is our future value. You will notice that I'm not writing S I'm writing F V because on the calculator it's written F V that is our future value. We are given the present value. Just give me a thank you all my people today they are on strike they are making noise. Okay. Apologies for that. Okay. So that will be our present value our periods remember it's N in this instance so I'm going to write the N just identify the things that you are given our period and we are also given the rate now. Here is the other thing that you need to be aware of especially those who are using a financial calculator when it comes to the interest you don't have to go and divide by a hundred only when you are using formulas you need you need to go and divide by a hundred here our interest which is I and Y that is our rate interest rate we're going to capture it on the calculator as we see it and here we see it as 7.5 and that's how we're going to put it on the calculator now we are ready to calculate but before that we need to finish off compounded yield so therefore it means our compounding periods and now I'm going to write compounding periods SP slash Y that is our compounded periods so that is equals to 1 now we are ready to go and write the steps so the first step we need to do is to clear our calculator from any stored values on the calculator and you need to do this step every time you use your calculator otherwise things are stored on your calculator and you are not aware of and then you just continue you will get the wrong answers so the first step that we do is press second function and then we press mode button which is the CA second function and the mode button which will be second function CA because we're calling the value that is on top of the mode which is written CA the next step is to capture the compounding periods so we need to know that the first step clear the calculator it clears the calculator second step we need to enter the compounding periods by saying second function I and Y remember we pressing the value on top of the I and Y which is P slash Y I and Y and then we're going to press the compounding periods we said it's I1 which means it's 1 so we're going to press 1 and then we're going to press I and T and our compounding period is start on our calculator and what is next is to press the red button the on and off and then we say on and off our calculator and then we go and press plus or minus always use the plus or minus so the plus or minus is that one plus or minus the present value you press 500 and then you press PV which is your present value the next one let's put in our interest of 7.5 you just go 7.5 and you press I and Y which will store your interest on your calculator you don't have to worry about dividing by the interest in the memory of the calculator it knows how to work with this data that you are storing the last step of entering the data we need to enter the year the period so there are 10 and because I want to multiply it with the compounding periods the reason why even if the compounding periods is 1 the reason why I'm doing this is to make sure that I remember the steps all the time because all the time you need to press multiply by the compounding periods you need to remember that otherwise at the later stage I will tell you that when does it not matter whether you need to do the multiply by the compounding periods but for this we're going to multiply by the compounding periods because we did put the compounding period as well so we say 10 second function n we press the n button which is the times p y you will see on top of the n button there is times p y and then you press n again so that you can store that data onto your calculator and once you are done then you can compute your future value which then you will say comp fv that will give you your future value so I want to give you 2 minutes to see if you can do the calculator and get the same answer and let me know if you are not getting the same answer so on the calculator I'm also doing it on my site so I expect you to follow me second function ca which is the mode second function in y which is p slash y and press button number 1 and press E and T and press the red button which is on and off press the plus or minus at the bottom of my calculator which gives me a negative value press 500 and then press pv always when you capture the value of your present value or your future value you need to put the plus or minus first if in your question there is a present value and the future value together one of them needs to have a negative value then plus or minus needs to be on one of them so for now plus or minus 500 pv and then we're going to put in 7.5 you don't even have to play your calculator you just continue and then press I and Y and it will store 7.5 on your calculator we say 10 second function button n and then we press also n again and then it will say answer arrow n is equal to 10 therefore 10 is start and then I go comp c o m p which is the gray or black button and future value and you will see that the answer that I get is the same as answer that we got the previous time which was 10 1030 .52 so I hope everyone got the same answer now just to close off before you start doing your activities and exercise as well if you do not have a financial calculator you need to know how to manipulate the equation this is the original equation you need to know if you need to make p the subject of the formula this is the way the equation will look if you need to make r the subject of the formula then that is how you will your equation will end up being because you will divide s by p and you will need to get rid of that power of t which means you will have to take the root of that the root of s over p and then you need to subtract one from the answer if it is the period that you are looking for all the time then you need to know how to make or bring t down by using the laws of logarithm on how to get t down by using the log and that is how you will calculate your formulas manually otherwise all the steps that we did here everywhere where you see red everywhere where you see red I can block it out and tell you that that is the values that you are going to interchange all the time except the on and off so those if you know the steps this will be the standard this is the step that we are going to always follow second function c a second function p slash y what is the compounding period e and t on and off plus or minus and this two can interchange the p v and the vf and the future value so plus or minus what is the value of the present value or the value of the future value i and y what is the value of i and y the p react second function times the compounding periods and store the value of n and compute compute present value of future value depending so the steps will remain the same so it means for every question you just repeat the same step writing them but substituting the right values on to the right place on the right place okay so let's do the easy one this is your exercise it should take you two minutes whether you using your calculator or you using your your financial calculator so i'm going to do this one and then the rest of the other questions you will do them yourself calculate an accumulated amount after three years if 5000 is invested at interest rate of 10 compounded quarterly now my question to you what is it that we are asked to calculate what are they asking us to calculate it's the future name the future value so therefore it means those who are using manual calculators you say s those who are using financial calculator you say vf what is it that they have given us after three years what is that it's our period right so it means this is our t or we can call it n what else are we given so i'm going to first start with the the manual once and then write the calculator once if 5000 is invested so therefore our p or we can call this pv is invested at an interest rate of 10% so our r of 0 comma 1 0 comma 1 or remember those who are using financial calculator in y of 10 what is compounded quarterly how many compounding periods do we have four there will be four so our compounding periods will be four or whether we call it p y is equals to four so now those who are calculating manually we use the formula s is equals to p times 1 plus r to the power of t remember always remember that r is divided by the compounding periods and t is multiplied by the compounding periods you can do this outside you can come here and do that separately and say three times four and come and substitute into r and you can also do the same here you can also say this will be 10 divided by four and that will give you r and the answer you get we just come back and substitute into the formula that we know which is this which is just r to the power of t oh sorry I used the wrong symbol and then the value the answers you just substitute so that is that those who are calculating using a financial calculator you are going to put in the values I'm not going to put the value I'm just going to write the step second function c a second function p slash y and I'm just going to put the blog you're going to tell me what you put there e and t and then you go on and off your calculator and you plus or minus the value of your present value and what is the value of your i and y and what is the value times second function n and again so you can press n twice I'm not going to write p slash y it's very p times p slash y it's very long I'm just going to say n and again because you're going to need to press n twice second function n and then n again and then you're going to come future value and then you tell me what is the answer but you can put your answer on the chat so I did most of the things so I'll wait once you are done calculating you can write on the chat which options or what is your final answer are we winning okay alright number two number two and we have also how we calculated it okay so those who are using manual calculators okay let's see how we calculated our p is 5000 that's what you wrote times 1 plus our r 10 divided by 10 divided by 4 is 2.5 right is 2 0.5 to the sorry to the power of our t 3 times 4 is 12 and that will be equals to you and that's what you said 6,724 0.44 you tell me if they are wrong those who are using financial calculator you would have said this is 4 and here you should have 5000 interest rate which is 10 and the period which is 3 and comp let's double check second function c a second function i and y 4 e and t on and off plus or minus 5000 pv 10 i and y 3 n again comp fv 6000 I also get the same 6,724.44 which is option 2 you see how easy it is now those who are calculating using the financial calculator all these 3 steps here at the bottom this step and this step you can interchange you don't have to put them in order as they appear from here you can start with the interest you can start with the period but the first 3 part those ones you cannot interchange they always have to be like that okay let's see if we can answer this question with a deposit of 1200 Deborah opened a savings account paying 5.8 interest annually compounded monthly she urgently withdrew a sum of 800 after 5 years how much will she have accrued accrued in her travel account 4 years after withdrawing 800 the amount must be rounded off to the nearest rent the question is too long and too weighty but we need to find out what is it that we need to be calculating here we need to be calculating how much will she have accrued in her travel account after withdrawing the amount so how much it means the future veil accrued it means future veil so that is what we need to know what will be that amount in her account at that point but that doesn't say the accumulated amount it's the final thing so we need to also go back and read the question again so that we identify and make sure that we know exactly what is happening sometimes also it's easy when you use a timeline to identify certain things so we know that they deposit at this point they deposit 1200 into their savings account and that ends them interest I'm gonna write the interest of 5, 8% that is the interest but it is also compounded which is the compounding period monthly what is monthly how many periods is monthly how many periods is monthly 1 it's 12 they also tell us that she withdrew the sum of 800 after 5 years so this 1200 went up to there let's call it 5 years there so 1 2, 3, 4, 5 at this point they took out 800 so they took out 800 I'm gonna put it in brackets so that it's taken out but also when we read the question it says how much will they have in the travel account 4 years after they have withdrew the 800 so after this point 1, 2, 3 4 years after that which is 1, 2, 6, 7, 8, 9 which is 9 they want to know at this point how much they will have in their account so there are a couple of things that you need to know and need to do in order for us to find out what is that value that we need there after 9 years is the following we need to calculate the future value up to this point we need to calculate how much at that point she would have accumulated that is the first one once we have we need to also calculate the future value up to that point we know from here we take the balance after we take out the 800 so the balance after we take out the 800 of the future value so it will be future value minus 800 which will be equals to the balance we need to take that balance and calculate what will be the future value at this point so let's do that let us do that S is equals to we already stated that that is our P so the balance here will be our P at this point but now we are calculating from here so S is equals to P times 1 plus R to the power of T you do the thing and you show me at the end how you calculated it second function C A second function P slash Y and you tell me how many compounding periods are there E and T on and off your calculator plus or minus and then you tell me what is the present value that you are going to put there and say that is the present value and you are going to put there I am going to switch it up second function and again and I am going to put there I slash Y and you are going to comp future value so that is what we are looking for you are going to comp future value once you are done with that then we need to calculate we need to subtract the 800 so once you are done with this then you are going to say minus 800 and you are not done you are not done with that 800 so now all what you need to do right now is to write the answer that you have there the answer you write it down then you will come here and you will say plus or minus and then you will put the answer that you have there into that and you will press the pv and you will come here to the second part only you will press the period here you said it is after for yes remember the period here and the periods here are different so you will put there for and then you will say second function and you will say n and again and then you just say comp and then you say fv those are the steps that you do on this side you will calculate and then you will get the value of s and you will say the answer you get there and you are going to subtract 800 there and once you have your 800 there you are going to also go back to say the answer you get here you are going to say the answer you get there it is your present value so that will be your present value you are going to calculate again s is equals to your answer I am going to write the answer times 1 plus your rate which will be your rate depending on how you calculated your rate remember the rate is 5,8 divided by compounding periods you just always have to remember that to the power of your period which is t times 4 here it will be t times 5 and the rate will be divided your t here is 5 sorry my bad t times the compounding periods and so forth so let's see what you did and you need to tell me what is the answer so I gave you the steps I expect you to do the work I will check the yeah you did the first step you need to take the answer and make it your present value now and recalculate but now using that as your p is 802 and your t now no longer going to be 5 but it is going to be 4 you need to do the next step and Candice I guess you are using a financial calculator the way you are so quick and fast are we winning and I hope you are writing all the steps down especially those who are using financial calculator you don't rely on what I wrote but you also write it on your your book hi Luzzie I must step after the pv what do I write before second in in yes what do I put there here you are muted am I muted all the time yes you are muted you guys you don't even say I am muted no we thought maybe you just wanted to do the calculations and then after that you will explain oh no I was explaining so it means I was talking to myself alright so for those who are using the calculator then this is how you would have wrote the steps right the accompanying period is 12 plus or minus 1200 is your present value 5 is how long because that is how long 5.8 remember we write it as is it's 5.8 it's interest then we compute the value of future value you will see in front of your calculator you will have 5 8 0 2.59 and some few numbers right you need to just say minus 800 and that will give you an answer and write it down and that answer will be sorry when you say compute future value it will give you 1600 and some number so let me just calculate it quickly because I don't have it in front of me as well I and Y 12 E and T and on and off plus or minus 1200 that is present value 5.8 that is I and Y and 5 second function N and again that is the period and comp future value you will get an answer off when you say comp future value you will get an answer of 1600 and 2 so which this is also wrong this is also wrong because I'm using the wrong answers 602.5 sorry 602.5 9 30 something like that subtract 800 and that will be your present value you just the answer you get from subtracting that so minus 800 that gives you 802.59 that you will write and put there and you say that plus or minus the answer you got there that will be your present value and for second function and and again that and then say compute so you just click on on what I just said plus or minus without even going anywhere plus or minus 805 or 802.59 and you press PV and you just press 4 and you say second function and and again that will give you the compounding periods and you say comp future value and the answer you get will be 101.5 9 66 but they say round it off to the nearest rent so that will give you option number 3 those who are calculating manually you just substitute and calculate then you will get 602.5930 and some numbers and you take that 1602.5930 and subtract 800 and you get 802.59 and you substitute and you will also get 10 1 what did you get what did you get Pelo 11.6 that's what Pelo get 11 because they round it off to 1 Decima 0.6 but we want it to to to a nearest rent so it's still going to be 112 so that's how you will calculate their compounding periods let me leave you to this one I'm not going to give you some hints or anything here you are asked to calculate they say same invested 6800 at 12% interest per annum compounded monthly the number of months he has to wait to invest the amount to grow to 9165.32 or 37 rounded to 2 decimal will be so they want the number of months not in years but your periods so because it is compounded monthly so the answer you get when you calculate so you will need to use s is equals to p times 1 plus r to the power of t they want t make t the subject of the formula second function c a they can function e slash y and you need to put in your compounding periods and press e and t on and off your calculator plus or minus remember you are given two numbers present value future value one of them needs to have a plus or minus in front so we can put the present value first and then do the future value second what else are we given interest I'm just identifying them by looking at the questions so this is your present value this is your future value this is your rate and it's compounded monthly so it will be 12 and we are asked to calculate t so we need to comp and that's what we need on this side on this side to make t the subject of the formula we need to find s divide by p 1 to the power of t and if I take the log so this will be the log of s over p this side and this side will be the log of 1 plus r to the power t and t can come in front log of 1 plus r log s over p so this is what you do before you even start calculating because you want to make t the subject of the formula so therefore it means the formula that you're going to be using is the following I'm just going to write it here at the top I'm going to remove all this and write the formula because that is the formula you're going to be using it's log of s over p divide by the log of 1 plus r is equals to t that's what you are looking to use to calculate so for both I have given you if you don't know where to find the log on your scientific calculator you must look for it it might be written in orange or it might be written on the calculator as is it is just log like that it's written like that on your calculator okay we have an answer it should be easy and quick and easy so okay the question you asked in the in the chat about HOMOTO buying a townhouse that is for next week when we deal with annuities you can bring that question again but I think it's also on the on one of my loads I'm not sure but you can bring that again next week or you can post it on whatsapp and then I will add it on to the activities for next week we dealing with annuities so number one kendis says number two Gihilo says number one so let's see if it's number one if it's truly number one let's change colour of my pen okay so how many compounding periods we said there are 12 present value it's 6800 future value it's 9165 0.37 interest is 12 second function CA second function INY 12 ENT on and off plus or minus 6800 that is our present value 9165 0.37 that is our future value 12 that is INY N that is equals to date and that is dating 30 months if there we have said INY you will take this dating months divide by 12 if it says INY and it's compounded monthly quarterly you will divide by 4 if it says yearly you will divide by 1 if it says by annually you will divide that 30 months by the compounding periods only when they say the number in years if they say so then you divide by the compounding period so for now they just want it in the same month as the compounding period so in terms of the lots so log of our future value is 9165 0.37 divide by 6800 right divide by the log of 1 plus our rate yeah it's 12% so it's 0.12 divide by our 12% which is equals to t and I'm going to assume that the answer you get here from calculating the whole question will be equals to t will be equals to 30 as well let's see on the answers so can I please have your number Ms. Bowie for the WhatsApp group okay I will share the WhatsApp group just now which means it is option number 1 okay I also have this one question as well but I'm not going to ask you to do that in the last 15 minutes that we have I just want to go through one of the other important activity that links to compounding periods is time value of your money I'm not I don't expect you to go and do some calculations because it's everything that we have done is just that you need to know when to move money backwards or forward this is only relevant to those who are doing BMI but if you do in BNU this year therefore it means next semester you will be doing QMI or next semester you will be doing QMI stay behind and see what we're talking about so that then it refreshes your mind that time you look at the same information so time value of your money is when you are negotiate whether you want to change your agreement date you want to move your money forward meaning you are struggling with the payments and you want to make sure that you pay in the future than the agreed time you want to move your money backwards meaning you now want lotter and you want to pay off whatever you owe or whatever you loan and that is what time value of your money is and it's also based on the principles of all the concepts of present value and future value there's nothing wrong with that so there are two rules that you always need to remember with this to move money forward it means you're going to inflate the sum by multiplying by the accumulation factor so the accumulation factor is the same as the one that we have been using which is from the future value is p times 1 plus r come on rt so that is moving money forward we have been doing that with the compounding periods activities or exercises that's what we've been doing moving the money forward moving money backwards that's what we're talking about here with time value of your money so we want to move money backwards so when we move money backwards we're going to be dividing by the accumulation factor which is that we divide by that meaning we can multiply by the inverse which is minus t you can see that it's the same by minus t there then it's the same as multiplying by the negative by 1 over sorry so this will be the same as s is equals to p divide by 1 plus r to the power of t that is moving money backwards so we can do this way or is the same as s is equals to p times 1 plus r to the power of negative t those three equations are one and the same thing so moving money forward we use the standard equation moving money backwards we use either we multiply by negative t and the accumulation factor of the discounted factor or we divide by the accumulation factor that's what we do okay and in terms of moving money there are there is a concept of obligations and debts and payments so it means the number of payments should cancel out the number of debt or the number of obligations you have and let's look at an example if n had to pay his father 7000 which was due in four years time to lessen his burden he pays his father 11300 in advance at the end of year one after some bad luck he had to go in Boru an additional 708 from his father at the end of year two he decides to live a debt free life and pay off the entire loan at the end of three years the payments and the debts are subject to the same interest namely 11% per annum compound debt what will be the final payment at the end of year three if you look at this you might think oh but here we're talking about annuity no this is still compounding interest so sometimes you can draw a let's draw first a timeline like we did with the other one so we know that he went and he borrowed 7000 at the beginning but it's due at the end of four years let's put four years there so this is year one at the end of four years that 7000 is due there it needs to end at that point to lessen his debt he pays and then he goes and he pays at the end of year one so year one this is zero and there goes year one at the end of year one which is the beginning of year two at the end of year one one two three four at the end of year one he pays 1300 so he's still left with three years to go after some bad luck he had to go and borrow so he goes and borrow at the end of year two so there is year two he goes and borrow money since I don't have a ruler my thingy let's redraw the lines properly year still so this one we know that it will end there at the end of year two we know that that starts but it needs to go some way I don't know we don't know whether it's going to end at year four or not right because they didn't say when he's going to pay that he decided to live a debt free life for the entire of the entire loan at the end of year three so there is year three he decides to finish off at that point the payments and the debts are subject to the same interest of 11% so we know that our interest there is 11 11% per annum so that one is clear but it also compounded yearly so it means it's every year so our compounding periods which makes things easier it's one now we need to determine this so the payment because it's also included in the interest it will stop right there so it's moving forward so since it's moving forward then it means we're going to be calculating P times one plus R to the power of T because it's moving forward we're going to use that formula the debt free the 780 the 780 it's also moving forward but because it's going to end there so this will also be P times one plus R to the power of T the 7000 remember it was due at that point now it needs to move so but when it moves backwards it moves backwards this way so it will move backwards so it means it's P times one plus R to the power of negative T now you need to also include the T's in every one of them so for the 7000 in state of counting from one to four we say how many times it's moving forward it's moving backwards so it's moving one time our T here will be equals to one our T here it's also going to be equals to one our T here because it's on the second year or at the end of the first year so we're going to count one two it's moving forward two times so our T here will be equals to two and we can just use it this way debt equals to obligation sorry, payment equals to obligation so our payment was 1200 plus our final payment that we need to make our debts we know that it was a 7000 plus the 750 now we can write the formulas in terms of what we know we know that some of them are moving forward some of them are moving backwards and those are the formulas that I've put in and you can just calculate so we know that the 1200 is two times so there is the period because we also multiply by the compounding period of one so it's two and our R is divided by the compounding period and all of them are have the same interest of 11% so divide 0,11 by one is 0,11 so our debt of 7000 it's moving backwards once that is what it's moving backwards and the 780 as well at the end of the second year it's moving only one time to the third year so we can then just substitute and calculate and manipulate this so that we can only be left with final payment and our final payment is equals to 5,708 780 so you just need to know how to do this if you are using your financial calculator it's the same thing you just write the formula because we know the things that we need to be calculating write them down but use your calculator use your your steps to do that so you can write payment of deposit 1,300 and the final payment it's equals to the debt of 7000 plus the debt of 780 and then write the steps of each one of them so you can see that this is the step for the 7000 those will be the step for the 780 and that is the step for the 1,300 what is more important is when the money is moving backwards always remember to also use the plus or minus so this minus you will use the plus or minus the same way as you use the plus or minus there to put that so this negative here you can just use plus or minus to put the negative in front and we will get the same answer as the previous one and that is time value for money so these notes are uploaded on the on the platform and the classes happens every Monday from now on until you go write the exam we will be having classes you will notice that I do have lots and lots of other exercises that you can do to practice if you do these exercises you can share your answers on the WhatsApp groups or you can email me and I will gladly help you sort it out I haven't forgotten about the previous activity actually I forgot not that I haven't forgotten I forgot that I promise that I will send you on the WhatsApp the solution to that I will also post it on the WhatsApp groups as well so you can see how we answer that question that we couldn't do the last time I forgot about it I will do it tomorrow as soon as I am free and then I will upload it I just remembered now when I saw Paolo asking a question there do you have any question before we wrap up this session and any question any comments Good evening Goodwin Yes I just joined you a little bit late but it was before but I say now that it's from 1800 hours up until to 1980 hours so it's actually one and a half hour as you say you will upload up the previous sessions because I think I missed the last session you are going to upload them on a platform or on the WhatsApp one thank you I will speak about that one just now as well I have uploaded the register on the chat please make sure that you look at that the WhatsApp groups sorry I am going to get you the link so make sure that when you join the WhatsApp you use there you use the correct link I can't find the I can't find the links I don't know I have placed the links just give me a second I will find the links for you how possible does anyone have the links since I can't find the links oh I do I have them please make sure that you join the correct group as well I am going to share the first one is the QMI link if you want to join the WhatsApp group and then the second one is the the BNU please make sure that you complete the register as well please can you go through the example of the last example we just did we did next week unfortunately I cannot repeat the session so once we've done with once we concluded this then we done next week it's a new session there are not linked however you are more than welcome because there are activities as well on on the handouts in terms of value of your money there are a couple of exercises so this is one of them so there you can see obligations you can do those exercises the two exercises and we can have a discussion on WhatsApp how to answer them and show me and you can show me how you answer those questions as well and then I can give you feedback and yeah so unfortunately next week we doing because we only have one hour and 30 minutes we doing annuities as well so next week I'm going to show you how to answer questions relating to annuities and then yeah so let's come on because I need to close up sorry my bad okay so let's recap and check in with the session in this session you've learned not the simple interest but we've learned compound interest and rushed through with the last 15 minutes but at least have an idea in terms of what time value of your money is what is very important is that your financial calculator if you don't have it there is no need to go and buy it but it is a must to have this two sessions that we had the simple interest session and the compound interest sessions you can still go get away with not having a financial calculator when we go and do the annuities and then also do amortization you cannot you will require the calculator because sometimes they can ask you to calculate or calculate the balance at the end of 62 years how would you create an amortization schedule for 62 years or even if it's 24 months or even if it's 12 months it's going to take you forever if you are using a manual calculator but if you have a financial calculator it will be very very very useful because you will finish your exam on time and not panic as well so when using a scientific calculator remember to use your formulas identify what you are given in the question be able to identify the things that are in the question and the right formula because remember when you go and write the exam it's not going to say compounding this is where you use the compounding interest you just need to make sure that you read the question and identify that this is a compounding interest it's not an annuit because there is a that small little thing that changes from being a compound interest to an annuit it's easy to identify simple interest because they will tell you that it's simple interest and you will know that you will need to use simple interest but when it starts with compounding interest and when you're doing annuities and when you're doing amortization all of them use simple interest so you just need to know how to identify the questions in order to select or use the correct formula as well when it comes to time value of your money you need to always be mindful that if you're moving money backwards you need to multiply or use the discounted factor or you need to multiply by a negative accumulation factor what else and that's it from me any questions for me it's just a comment it's been always a pleasure to be on this platform even if I translate but I manage to grab up something thank you for your effort no problem now when it comes to the notes and comes to the recordings the recordings are shared to say the recordings are always shared on the way you find the schedule and finding the schedule I always say you need to keep the links that I share with you because those links are very important some of them have important information so the link that I shared I'm not sure if I did share it now with you on this call but I just want to show you let's see if I can so there is a link that I always share with people in terms of I've created a short link for it I can also share that with everyone again on this call so that you know where to find everything so I'm posting the same link there right so that it's part of the recording as well I want it to be there so when you click on that link it will open up this schedule on the schedule even if you don't attend a class or you miss a class you can still go back and find your notes so today it's Monday unfortunately the schedule cuts off they don't load it for the whole month it's only for a week so as you can see start from Monday and it ends on Saturday so today it's Monday you will be able to see Monday's events and this is our event basic numeracy skills and when you click on join session it's where you will join the sessions all the time when you click on notes and recordings it will come to this platform unfortunately they haven't loaded all the recordings this first recording as well it's cut off because somebody stopped the recording and they never gave us some what do you call that permission to download this so UNISA uploads this recordings for you so you can come here but I can see that we missing so many of them so already now I think the second I'm not sure if we had another one before this but there are recordings missing from here I'm gonna guess no it's only one so we had the 11th which is half cut off then you have the 25th which is the one that we had and then last week's one I think probably they will load it on here so you will find last week's one and then this week's one will also be loaded here but it takes long to get there the notes before the session every week I will load the notes if I have the notes when in advance I will load them here for you but here are the notes as you can see there are today's notes there and this is the note that we were using today so you just click on the links so if you click on here it says open class notes folder you just click there it will open the folder on your side it might not look the same way as my one but you will be able to see all the notes that are shared with everyone you can access them there thank you just hold on don't go anywhere and don't go anywhere and I'm going to stop the recording and thank you for being part of the session today bye don't go