 So, please, do not forget to complete the register and then we can start with this week's research. This week, we're going to be looking at annuities and we'll do a lot of other activities just to see how we calculate annuities. And remember, we're going to still continue doing manually and also using your financial calculator if you do have one. It is eight minutes past, but I can ask, do you have any question or comment or query that you want me to address before the session starts? The register, ma'am, did you post it? Is it in the chat? Yes. Thank you. Like I said, this week, we're going to be looking at annuities. You need to have a calculator and you need to know the formulas to calculate or for calculating annuities. By the end of the session today, you should be able to do basic calculations when it comes to finding the present value of an annuity or the future value of an annuity. What do we mean by annuities? Annuities are just payments that you make at a regular interval or at the regular time or period. So it is your sequential equal payments at an equal interval of time. So for example, when you, if you have a loan at the bank, so you know that you always go into, you sign an agreement to say you're going to pay, let's say 3500 every month. So that will be your equal payments at an equal interval. Your interval will be the monthly payments that you are making and your equal payments will be those 3500 every month that you are paying. So those we call them annuities. Anyway, we can also refer to them as payments. So your payment interval will be the time between the successive payments that you are making. And this also depends on whether you pay monthly, quarterly, yearly, by annually and so on. The term will always refer to the period, how long you are going to pay that annuity or that payment. And it is always from the time, from, it starts, you start calculating it from the beginning of the first payment up to the end of the last payment interval. Your future value will be the cumulative amount of the payments that you have made, including interest. So it will be the sum of all payments made, including also the interest at the end of the time. And your present value will be the sum of all the payments that you have made. And these are each discounted to the beginning of the time. So how are you going to remember this in a way? You need to remember that savings, you get money at the end, right? It's savings, you only get accumulated amount, which is your saving amount that you have accumulated at the end. With savings, if they talk about saving, saving, saving, always know that you will be calculating the future value. Most of the time, loans, which are the money that the bank give you, it's now, now, now, now, it's already discounted amount, right? They tell you that you apply for a bond to buy a house and they tell you that the bank say, I can give you one million for that house. But you will still need to pay me, including interest at the end of the time when you finish off paying your bond. But because the bank is giving you money and that we call it the present value. So how you will remember savings, future value, loans, present value, right? If they give you a question and they talk about savings, you need to know that you are given the future value. If they say Patrick saved 100,000 or needs to save 100,000 after four years, that 100,000 is the future value. It's something that they will need to save up for. If they say Patrick went to the bank and the bank gave him the loan to buy a car, that loan is your present value. Because the bank gives you the money now you have the money to buy something with it. Then you will be calculating the present value, right? With annuities as well, like we did with compounding periods, you still also need to know your compounding periods because if it's compounded monthly, therefore it means also your payments will be made monthly. If it's compounded quarterly, so your payments, you will pay your, you will do your payment quarterly. If it's yearly, you will pay your payment yearly. It's very important to know your compounding periods because they affect how you multiply your period because your period needs to always multiply with the compounding period and or your time needs to multiply with the compounding period and also your interest needs to divide by the compounding period. So it's very, very important that you know your compounding periods. Okay, so in order for us to calculate the present value of an annuity and I must say also with this formula, you are still going to use it when you do amortization because amortization is based on the loan and therefore remember what I told you just a minute ago, loans are always present value. So when we deal with amortization, you are still going to use the same formula to calculate your payments. So to calculate the present value of an annuity, we use p is equals to r times the accumulation factor of 1 plus interest to the power of the 10 minus 1 divide by your interest times 1 plus your interest to the power of n, which is your 10. Now, you're going to ask how do we calculate this? This is just a short version of writing the accumulation factor and you can write it when you are using your financial calculator to do the calculation because you're not going to substitute the values. So you can just say p is equals to r times the annuity of ni, which is just the accumulation factor of an annuity for that payment. So we're going to learn how to use this formula to calculate the present value of an annuity where your r is your payment and the other like your i is your interest, which you need to divide by the compounding periods and your n is your term, which you need to multiply by the compounding periods. p is your present value. So if we need to calculate the present value of 1,600 quarterly payments for five years at an interest rate of 20% per annum compounded monthly. The question is asking us to calculate the present value. What are the effects given in the question? We are given quarterly payments, which means we are given our payment, which is our r of 1,600 and they say it's quarterly payment. So obviously some way they will tell us that it's compounded quarterly. If they didn't tell us that it's compounded quarterly, we can assume that this is compounded quarterly. If they gave you a compounded value, which is different to the monthly payment, therefore it means your monthly payments, you will need to change them or convert them to the quarterly payments or whatever the compounding periods are, but usually they are aligned. And what else are they giving us? We are given five years, which is our n and we are given our interest, which is our y. And we are told that the compounding periods, they are quarterly, so they will be four of them. Now I need to identify the formula. I know that the formula that we need to use is p is equal to r times the accumulative factor of an annuity. Then we can substitute into the formula. Remember, your interest needs to be divided by the compounding periods of four and your period needs to be multiplied by five. So you can do this outside because if you put it into the equation, your equation will be too much. So for example, like I did it, I included my division of the interest and multiplication of my term in the equation, as you can see, it looks complex. However, if I could have just taken 20 percent, which is 0.20 divided by four, which will give me 0.05 or 0.5. What is 4 divided by 0.20 divided by four? Let me use a calculator because it has been a long day. So let me not over stretch my brain. 0.20 divided by four is 0.05. I was right there at the beginning. It's 0.05. I could have substituted 0.20 divided by four by 0.5 and five divided by four, so five multiplied by four is 20. I could also have just substituted there by 20 instead of substituting into the formula as well. So the formula would have looked like this. 1,600 times 1 plus 0.5 to the power of 20 minus 1 divided by 0.5 times 1 plus 0.5 to the power of 20. And when you simplify the whole equation, you get the present value of this payment, which was made quarterly of 1,600. The present value is 19,939. So that is if you don't have a financial calculator, you can calculate manually by using this. If you have a financial calculator, you can do the same by following the steps. So also, on your financial calculator steps, you also need to identify what the question first, what is the question asking you to do in your own time? They are asking us to calculate the present value. So I'm going to say they are asking us to compute PV because I'm looking at, remember, the functions are the same. We're still going to use those three functions, or those functions, the first line function, the ENT, the plus or minus, the mode, the ON and OFF, and the second function. All those are our friends for now. While we do this, as you can see that they're the same functions that we used previously as well. So we are computing the present value. So that's what we need to be computing PV. What have they given us? They gave us the payment. Now on your calculator, there is no R, it's PMT. So they have given you PMT of 1500. The number of years is N. There's a capital letter because that's what on your calculator you see. And your rate is I slash Y. And remember, those who are calculating or using your financial calculator, I and Y is 20. We keep the percentage. If you are calculating manually, you need to divide it by 100 or you can use your function on your calculator. So now I have everything I need. Then I can write my steps. It's very important to first write the steps before I can take my calculator and calculate. So the first step I need to clear my calculator from any stored values. That is the very important. Remember that. Clear your calculator from any stored values. Step number two, we need to capture the compounding periods. So our compounding periods or I didn't finish our compounding periods, which is P slash Y. It's equals to four. So our compounding periods, they are four. So we need to capture them. So second function, P slash Y, four is our compounding periods, ENT. The next step is to go on and off our calculator. And then we need to capture what we are given. So at the moment, we're given payment and number of years and interest. Now there is no order in which you can put anything that follows here. So we can start with interest. We can actually say 20. We can say 20 INY. And we can go and say plus or minus the payment, which is 1,600. And we press PMT. And then we go and say five years and we press second function. Remember, we always have to multiply your period by the compounding period. Second function, N and again. And I'm saying N and again because the first second function multiplies with the compounding periods, which is the yellow part. And then the second N is to capture or to store your value. And once you are done there, you can comp. And then you say PV. It will give you the same answer. Or you can start with the payment first. You can start with the payment. Remember, for payment present value, any one of them, only one of them. If they are two of them, one of them should have a plus or minus before. Otherwise, you will get a negative answer. Always remember to press the plus or minus. That is the plus or minus, not the negative and positive or the plus sign and the minus sign from the basic operations. The plus or minus function. So we put the payment. Then the next part is to put in the number of years, the time. Five second function and energy. And then we put the interest 20. We put it as we see it 20. And the last part is to comp PV, which will give us 19,939. And now, once you have written your steps, then you can take your calculator and start calculating. And that will be it. You. They've answered your question. And that is present value of an annuity. Your exercise. Let's see if you listen to me. What is the present value of an annuity of 1500 payable at the end of six months period for two years? If the money is worth 8% compounded semi-annually. You've got two things here mentioned. Six months semi-annually. What is it that they are asking you to calculate the present value? So let's start first with the manual. So we need to comp compute or calculate. I'm going to make it like this because on my rough paper. I'm going to say my P that's what I need to be calculating. They have given me my payment, which is 1,500. They told me my N is two years. They told me that my I is 0,08. And now I want to come to those three times. What is semi-annually six months? What is semi-annually? It means by annually, right? Because semi means two or semi means half. So if semi means half or two, then six months will mean half of the year, right? Because a year is made up of 12 months. If I split them in half, there will be six months for one. Six months for the other part. So they mean one and the same thing. You just need to make sure that you understand the terminology that they give you. Whether they give you by annually or they give you six months or they give you a semester or things like that. Things that you can sometimes make sense of. But just broaden your mind in terms of the keywords that they might give you in the question. And try and make sense of them. So since our compounding period is two, therefore we need to divide our interest by two. We need to multiply our periods by two, right? That's what we know we need to do. So this will be equals to four and this will be equals to zero comma zero four. Because zero comma zero eight divided by two will just be zero comma zero four. Your formula that you need to be using P is equals to your payment times one plus your interest to the power n minus one. Divide by interest times one plus your interest to the power and and you can just substitute into the family. Now go into those who are calculating using your financial calculator. You do the same. You are asked to come. You can also just write PV. You need PV. You are given PMT of 1500. You are given n. Two years you are given I and why. Of eight. That's how you will write it. And what else? Your compounding periods. Your P slash Y of two. Remember the steps. I'm not going to substitute the values. You need to substitute the values. I'll write the steps for you. It's second function CA always get your calculator. Second function. P slash Y. Where I put the blank, you need to know what you need to put in there. Because I'm not going to give it the value just yet. And then you need to go on and off your calculate. Then you go plus or minus. There should be a value somewhere here. Which corresponds to your PMT because that's what you are given. And there should be a value here. Cross body to your interest. And there should be a value here. Which you need to multiply by the compounding period. And store the value. And then. Come. The steps are almost exactly the same as the previous one. Instead of using the payment and computing the future value. We just put there what we are given and computing whatever we ask to compute. Are we winning? Just a second ma'am. I just wanted to check if I am not losing you. You are not confused. I got 6,000. Are we done? I'm done. And I think Lesley is done as well. For the first time I actually got my calculator to work with me. Thank you ma'am. I 4484. That's what you say the answer is. So let's see. If the answer is wrong, I'm sorry. Okay. So your R is 1500 times 1 plus. I'm going to use the value that we just calculated. Which is 0,04 to the power of 4 minus 1. Divide everything by 0,04 times 1 plus 0,04 to the power of 4. I don't know what the answer is there. Those who calculated using the financial calculator. You would have put here 2. You would have put here 1582. Let me double check with my financial calculator. Unfortunately financial calculator. I cannot demonstrate because it's an actual calculator. I don't have a tool to read it. It's easier for you to be able to see. So second function, CA, which is the mode. Second function. P dash Y to enter on and off your calculator. Plus or minus 1500. P and T, 8, I and Y, 2. Second function, N, N again. Comp, TV. The answer I get is 5,444 and 84.84836. So we round it off to 2 decimal because it's money. Money always be rounded off to 2 decimal. So it's 5444 comma 84, which is option 2. Leslie, you got it right. Well done, Leslie. So let's move on to how we calculate the... That's too late. How we calculate the future value of an annuity. Remember, present value was loaned. Future value is savings. So calculating the future value of an annuity. We use this formula. S is equals to R times 1 plus I to the power N minus 1 divided by I, where R is your payment. S is your future value. I is your interest. N is your time. Let's look at an example. Jack will need 20,000 to buy his brother's car in two years' time. He wants to start saving part of his weekly salary into an account that retains 8.5 interest per year, compounded weekly. Calculate the minimum weekly payment that he needs to make into the investment account to have enough in two years' time. Very long sentence. Okay. So what is it that they want us to calculate here? The question is asking, calculate the weekly minimum payment. So it means they're asking us to calculate R. Not like the previous one, where they were asking us to find the future value or sorry, the present value. They want us to find what will be that future value or what, sorry, what will be the payment, not the future value, the payment. So what is it that they have given us? Jack will need 20,000. So 20,000 it means at the end. We'll need 20,000. So 20,000 is our future value. Remember savings, future value. To buy this brother's car in two years' time. So I'm going to assume that two years' time because also in the question they spoke about two years, that is our period. Maybe I should not be using Fs and let's start firstly with the manual calculation. So our future value is S of 20,000. I did that because I've got steps here. Your R is what we're looking for. Your future value which is your S in two years' time that is N. And they say he's going to use his weekly salary, right? But we also know that it is compounded weekly and the interest which is our I and I can write it 0,085. You must write it the way you see it, all of it. Do not round it up. You must write it the way you see it. So this was two years. And our compounding periods, they were how many? Let me ask you how many? What are our compounding periods for weekly? How many weeks do we have in a year? 52. 52, yes. There will be 52 of them. So now what is the formula that we need to be using? That is the formula, right? Remember, you can divide your I outside divided by the compounding periods which there are 52. Multiply your periods by 52 and so on before you substitute into the formula and not follow what I do because I just put it in the formula. So our S is 20,000. R is what we're looking for. One plus our interest which will be 0,085 divided by 52 to the power of your N N is 2 times 52 minus 1 divided by our interest of 0,085 divided by the compounding periods of 52. And when we calculate this, simplify and the answer we will get would be because we just divide by the accumulation factor which is 118.23469 20,000 divided by that gives us 176 ranked 58. So from his monthly salary if he wants to make 20,000 in two years saving it every two weeks, every week, every week he will get 20,000 if he save 176 which will be option number one. So similar you can use your calculator your financial calculator to calculate the steps are exactly the same. What is it that they want us to calculate? They want us to calculate PMT which is payment. That's what they want. The weekly minimum payment. That's what we need to calculate. What are we given? We are given the future value. We are given how long which is our N. We are told what the interest is that is I slash Y. We are given the compounding periods P slash Y which they are 52. Now we can go and write up our formula. Play our calculator from NS dot values second function CA then put in the compounding periods second function PY 52 ENT on and off your calculator put in what you are given which is the future value. So plus or minus 20,000 future value in the interest 8.5 the period to second function N N again PMT when you come PMT your answer will be 176.58 Let's do another activity to understand. Find the lump sum that one must invest in an annuity in order to receive 1000 at the end of each month for the next 16 years. If the annuity pays 9% monthly or 9% compounded monthly. Now this question they've asked it in a way that it's not a normal way of asking a lot of questions like for example we know that we say someone borrowed money they need to pay it back or somebody is saving money and this is how much they will have and here they are asking you what will be that lump sum that somebody will get or somebody must invest in an annuity in order to receive 1000 rent. So that 1000 rent is a payment of some sort right it's an annuities of some sort so now we need to calculate what will be that lump sum that needs to be invested what is that saving that needs to be invested in order for it to receive 1000 at the end of each month for the next 16 years if the annuity pays 9% so ask yourself is this a present value or is this a future value it's a future value it's a present value this will be it will be the present value or the future value I hear two answers so present value seems like it's a present value because it will be because the 1000 you will be getting it for the next 16 years right so this lump sum should be your present value because it's something that you put in now it's not something that you need to be calculating for the future right okay so if this is our present value but it is an investment and we know with an investment we said investment are future future value so if this is an investment therefore this will be your future value always remember that savings investment are what we call future values so let's calculate the future value S is equals to terms because we know what payment we will be receiving from this future value of the lump sum that needs to be in plus I to the power of N minus 1 divided by I so you need to change your payment your N and your interest which is 0,09 compounded monthly so you will have to divide it by by 12 and those who are using financial calculator second function CA second function E slash Y what is your compounding periods E and T on and off your calculator plus or minus what is the value of your payment your interest and your period second function and again and comp what is it that you will receive after this that will enable you for the next 16 years to be able to get 1000 rounds every month are we winning? I'm not winning Me neither I want to try one more time I want to try one more time what is the value you are getting something not that but I'm going to do it again one second I'm getting 68 wait I'm going to do it again one more time hi we are looking for the future value of this lump sum because you are investing it right so it means at the end you will get something but it should that something should enable you to be able to get every month for the next 16 months 16 years for the next 16 years to receive every month 1000 rounds right so that S will be R of 1000 times 1 plus your interest of 0,09 since I didn't divide by 12 I'm going to include it in the formula and how long 16 times 12 minus 1 minus 1 divide by 0,09 divide by 12 and you will get that if you are using your financial calculator I'm going to change the color of my pen go back to my rate so your second function compounded monthly that's 12 payments 1000 of them interest 9 60 when you come that will be how much what do you get I know your intro thank you that's 12 instead of the 16 at the end which is silly I should have known let's look at more examples or more exercises a farmer needs 150,000 to purchase a 10 ton trailer the bank approves the loan for a full amount so the bank will give him 250,000 the interest rate is 18% per year compounded monthly the loan has to be paid off in 5 years time determine the minimum monthly payment we know that we looking for that's what we are looking for we are giving a farmer needs 250,000 the bank approves the loan of the full amount is this a present value or a future value present value loan are always present value savings always future savings or investments so this is our present value because that's the money that they will get now the interest is 18 which will be 0,18 divided by the compounding periods they are 12 compounding periods and how long 5 times 5 years 12 years we use the formula we is the present value so you need to use the right formula so for the present value so e times 1 plus i to the power n minus 1 divided by i times 1 plus i to the power n minus i to the formula your payment is what we are looking for your P is 250,000 your I I didn't calculate it so I'm just going to write the value as I have them if you have calculated it you will know which 5 times 12 is 60 I hope that I still know that 5 times 12 is 60 minus 1 divided by 0,18 divided by 12 times 1 plus 0,18 divided by 12 to the power of 60 because that one is easy to calculate take the accumulation factor divided by 250 you are taking your 250,000 divided by everything that is underneath the pattern those with a financial calculator second function ea second function p slash y put in the compounding period e and t on and off your calculator plus or minus 250,000 and that is your present value why did I give you the amount I usually don't give the amount because I'm giving you all the answers now and that you will be your i and y second function n again and off e and t let's see if you can get this one right when we are done you can just call out the number that it's correct think I'm done which one number 3 oh I got number 4 it is number 4 let's go back let's see the compounding periods they are 12 250,000 I've already given you 18 and the number of years they are 5 the only difference between when you calculate manually and when you are using your financial calculator is that your interest year you don't have to divide by the compounding periods because your calculator knows you also do not have to convert it to a decimal and you use it as you see it and the answer would be number 4 and I also see the calculator okay okay we train PMT to present value and at the end it's called not present value it's called PMT yeah okay so let's move to the next one cherry to take a family to a vacation in two years time suppose she deposited 192 rent 86 cent in the beginning of every week into an account earning 9.2 percent interest per year compounded weekly determine the amount she will have in two years time which looks almost the same as the previous one we'll start with the financial calculator one I'm just going to write I'm not going to identify what is given I'm just going to write the formula and then you solve it yourself and tell me which one is correct so I'm just going to write the steps down because it's very important to write the steps before I use the calculator now the challenge comes here because now I need to give you what is given so yet we are giving PMT but you just need to go and figure out yourself are we winning I'm done which one I didn't calculate so wait my bet you can just wait it will take me a second okay then which one number 4 so therefore it means you did everything right your payment is 192.86 times 1 plus your interest since I didn't calculate that is going to give me a very long number I'm just going to substitute the way I see it on the screen to the power of 2 times 52 which is 104 right 104 be fine minus 1 divide by 0.209 2 divide by 52 and the answer you will get here will be 22 000 0.005 which we rounded off to to 1 okay so let's see if you did calculate correctly and substitute correctly on the other side your compounding periods it's compounded weekly we have established that it's 52 your payment it's 192.86 your interest is 9.2 your period is 2 years and when you come it will give you number 4 happy are we good are we good or moving on to number 3 run out saved the total of 165,000 if every year he has deposited 28,500 into the account earning 6.04% per annum how long how long rounded to 1 decimal place did it take him to accumulate the total amount now you need to ask yourself what is it that they have given you and what are they asking you they're asking you to calculate how long the interest he deposited the amount in the account earning 6% per annum the accumulated amount and they're asking you how long since on year they didn't say anything about compounding periods but they are also telling you how often did they deposit the money therefore it makes it a annuity because it says every year he would deposit into the account this much on a sequential remember sequential payment at an equal interval yearly the payments were the same of 28,500 so we are told the future value which is also the S we are told every year means compounded annually our compounding period will be 1 the amount deposited which is the payment which will be your R or your PMT your interest which is your I or your INY depending on whether you are using a calculator or financial calculator or you calculating by your I N or N so right now based on this information the future value so we need to use the future value of an annuity which is S times 1 plus I to the power N minus 1 divided by I or we use second function CA second function even if it's 1 I always prefer to use the compounding period step so that I don't forget even in the future as well so you will see that second function P slash Y our compounding periods I'm just going to put the 1 since it is yearly and you can go on and off your calculator for a year you don't even have to do this step but I just like to do it anyway plus or minus you're going to put there because you are giving the future value and you are also giving the present value one of them can have a plus or minus so I'll use the 165 165,000 it will have my plus or minus and that will be my future value and you put in your interest which the 6,04 and that is your INY and you will put in the how long is what we don't have but we have the payment which is 28,500 that is our PEMT so I could have just done the PEMT before the interest it doesn't really matter pump we need the how long pump now I'm going to explain this later on as well let me do the site so we know what our future value is it's 165,000 our R is 28,500 one plus our interest now our interest needs to be divided by the compounding periods is it's one so it will be 0,0 0,0604 divided by one which is the same to the power of N N is what we don't know and this is where it becomes so complex because if you don't have a financial calculator this question is going to take you forever to answer it right because you will panic or give up from here 0,0604 I'm going to help those who don't have a financial calculator so we're going to take 165 divided by 28,000 so let's do that 165,000 divided by 28,500 which is equals I'm going to write only the answer to that I get 5,7 8 and you must write the whole of it don't take shortcuts equals because I've already done the division what is left here I need to get rid of the 0,06 so it means I must multiply by 0, I must take this multiply it by 0, 0 604 and what will be left will be everything that is at the top which is one plus this inside I can add them together as well and that will be 1,0604 to the power of n minus 1 what I can do I can bring minus 1 to the other side but before I do that let's multiply our previous answer multiply by 0,0604 equals and my answer this side is 0, 34 9 684 and I must take 1 to the other side it will be plus 1 is equals to 1,0604 to the power of n and if I add this side 1 plus 0, it will be 1, I'm just already doing the math and this 10 changes to 1, in order for us to get n down we need to apply the logarithm so we're going to say n times the log of 1,0604 and this side also the log of 1, 34 9,684 now to get n on its own we need to divide by the log so if I take this log divide it this side my pen is doing its own thing divide this side by the log of 1,0604 which means this side I will be left with n I hope you are able to follow and the answer will be equals to what will be the answer the log with my log on the financial calculator I need to go find my log where is it oh it's on button number 1 so second function log open bracket 1,349 6 did I miss a number I didn't miss any number 684 close bracket divide by the log function log of open bracket 1, 0604 close bracket equals the answer I get is 5 1, 1, 32 and they said round it off to 1 decimal and when you round it off to 1 decimal you get 5,1 yes if you also multiply or you do your financial calculator you will get your answer of 5,1 yes which is option 2 am I right so you just those who don't know how to use your calculator or you don't have a financial calculator you need to know how to use the logarithm I know that I took a shortcut but I hope you will be able to look what I have done when I was taking a shortcut because I don't have enough space here okay that's how you would have answered this question in your assignment because it was part of your assignment we left with 8 minutes let's see the next one Dineaud decided that she will save 3500 per quarter over the next 4 years she will make the first deposit into a savings account in 3 months time she will make her last deposit at the end of 4 years now at the end of 4 years if the interest is end at 6.68% per annum compounded quarterly what will be Dineaud's total amount okay sure let's read that again so that we understand and highlight the effect given so we know that we need to calculate the total amount which is whatever is it the savings yes for savings so it will be the future value that's what we need to be calculating Dineaud has decided to save 3500 so that is an annuity because they say per quarter therefore it means already they told us that this is our payment which is PMT over the next 4 years that is your end right she will make she will make the first deposit into the savings account in 3 months time so remember this is quarterly so quarterly take it into consideration 3 months equivalent to a quarter a quarter is made up of 3 months she will make her last deposit at the end of the 4 years at the end of the 4 years the interest end will be 6.8% per annum compounded quarterly so already we now know what our compounding periods are so our interest is 0.06 there are 2 successes so it should be 6.8 and you can divide that by 4 if you want let's see if I divide that by 4 how much I get so that I don't have to substitute the whole thing 0.0668 divide by 4 I hope it's not a long number yeah it's a long number but it's fine since I calculated it it makes it easy for me to use that 167 you need to keep all the numbers right and your 4 years which is your term so it will be 4 times 4 which is equivalent to 16 this is only for those who are calculating manually so let's do it for those who are calculating manually so this is future value so it's s is equals to your payment times 1 plus your interest to the power of n minus 1 divide by interest which makes it easier future value is what we are calculating you will need to calculate 3500 times 1 plus your interest calculated 0.0167 to the power of 16 minus 1 divide by 0.0167 and then you can go and find that those who are calculating using the financial calculator steps are the same second function c a second function p slash y what is our compounding periods e and t on and off your calculator plus or minus what is it that they have given us think the first one is the payment how long second function and again our interest y and y and we need to comp the future value let's do it for what so let's see if we can get it I will calculate manually you will calculate using your financial calculator someone will tell me how much what will be the accumulated amount so let's see I will start with the one that is inside the bracket 1 plus 0. so me I will calculate manually already have my answer I am waiting for you got number 2 nope is it number 2 check 3 yes I was going to have a heart attack I am thinking must I recalculate because I am calculating manually I am going to use the financial calculator number 3 is the answer the answer is 63 591 0.51883 which 2 decimal it will be 52 so those who have used your financial calculator your values will be as follows compounding periods there are 4 payment 3500 the year there are 4 interest 6.68 and you should also get the same answer okay one last exercise and then we are gone there are couple of exercises that have included but some of them they should be straight forward no body house for 1,000 oh sorry 1,300 in Victoria bottleneck she obtained a mortgage loan at 12.57% and I am compounded monthly with a time of 20 years her monthly payment would be so what is this is it future or present is it a present value or a future value a million present value it will be your present value your interest compounded monthly so your compounding periods there will be 12 right your time and your payment which is what we need to be calculating here I will start with the manual P is equals to R times 1 plus I to the power N minus 1 divide by I 1 plus I to the power N so our I is 0 comma 1 2 57 divide by compounding periods they are 12 can I just calculate that 0.12 57 divide by 12 is a very long number I am just going to write it here 0 comma 01 it might even be longer than the one I have because my calculator is on 6 decimal let me change the decimals display 0 tap 0 9 0 comma 01 04 7 5 you need to write all of them when you are using the manual calculations and your N will be 20 20 years times 12 which should be I think 210 foot right that is 240 let's substitute present value we need to start with the present value it's a million equals the payment that's what we need I am going to change the formula a little bit I am going to start with the payment I am just going to divide P by the accumulation factor so R will be equals to 1 million divide by the accumulation factor so I am doing it by surface which is 1 plus 0 comma 010 47 5 to the power of 240 minus 1 divide by 0 comma 01 04 7 5 times 1 plus 0 comma 010 475 to the power of 2 foot I shouldn't have put the bracket to restrict me so you will have to calculate that those who are calculating using the financial calculator you should get the answer before me second function C E A second function E slash Y what is your compounding period E and T on and off your calculator plus or minus they have given you a present value so you can just put the value of the present value what is the interest given and how long second function N and again and then comp E and T so I am going to use manual calculation you calculate with your financial calculator let's see who gets it first 1 0 0 0 0 0 0 3 million I hope there are enough I got number 4 hey you are so quick I am still going manual calculation you see it takes long but I will get there just give me few seconds I am almost done 240 my answer is 1483 4.026 which one did you get I got 1483 03 1483 4.026 which is 03 so you also get the same yes thank you very much especially if if you have a cashier you just need to also know how to use your cashier calculator so that then it doesn't take you long I use the fraction for the cashier calculator so I did the first fraction just to get the million and the bottom one and then I went back to the bottom one and I did brackets and then I included the fraction again inside the bracket so I hope I had my calculator on so that I can show you how to do that but next week when we do amortization I will try to activate my calculator online because it keeps on booming out especially with the load shading my calculator doesn't hold any longer so it bumps out every time I need to activate the license so that is a new it is actually and I have also included in the notes with you guys in the notes section additional other information but some of this because amortization and annuities they relate in terms of present value payment so we are going to still you will see that some of these exercises you might also see them again next week when we do amortization because we are there then after calculating the present value of a load we need to amortize it so you might see that especially when we deal with loads so anyway there is questions exercise 6, exercise 7 which comes from your assignment I think you can go through that again if you are not sure when you are submitting your assignment now you can go back and see if you are doing the right answers now so in conclusion we have learned how to do basic calculation when it comes to future value of an annuity and the present value of an annuity I will see you next week have a lovely lovely evening and enjoy load shedding and I guess today it was good for us because we didn't cut off due to load shedding thank you very much please remember to complete the register and bye bye bye