 to your fifth session. So today, please remember to also put what you call that now, complete the register. Let me first quickly post the register on the chat. Let's give me a second. What is the register? Okay, please make sure that you complete the register. And we can start with today's session. So today, we're going to be talking about annuities. You're going to learn skills on how to answer questions relating to annuities. Do you have any questions before I start with this session? Okay, in the absence of any question, then we can start. For today's session, you also need or you require your calculator and your financial calculator, EL738 calculator. Those with no financial calculator, then you need to know how to use your formulas and identify your formulas, the correct formulas. Okay, so by the end of the session today, you should be able to learn how to do basic calculations when it comes to annuities. You should be able to calculate the present value of an annuity and also the future value of an annuity. Annuity is just sequential payment made at an equal interval. So these are just payments. And also the payments that you make at the payment interval are also referred to the time between successive payments that you are making. So it means if it's compounded monthly, therefore it means you're going to be making payments on the monthly basis. If it's quarterly, you're going to be making payments on a quarterly basis. If it's yearly, the payment will be yearly basis. The time will be for how long you are going to pay or how long you are going to save. So this is the time from the beginning of the first payment until the end of the last payment that you have. Future value of an annuity will refer to all accumulated amount or the sum of all values or payments made. And this also includes the interest at the end of the time. And your present value, this will be your sum of all the payments that you are making and each of them being discounted at the beginning of the term because then that does not include interest. Like with the compounding periods, with annuities as well because you are going to calculate it using the compounding periods for how many periods you are going to make those payments, they are compounded. So you need to be able to know the compounding periods. I'm not going to go through all of them. We've covered them the previous time. So it is just to remind you that we're still going to work with compounding periods. So in terms of calculating the present value of an annuity, we need to be calculating payment and the payment in this instance is R. So P will represent your present value. So the present value of an annuity do not ask me what this symbol is. It's a shortcut symbol to calculating an annuity. So as you can see, then it says payment of an annuity based on the number of times and your interest. So this, don't ask me how do you calculate that because how do you calculate that? It is this formula there, which is R times the accumulative term, which is 1 plus your interest to the power of your 10 minus 1 divided by interest times 1 plus interest to the power n, multiplying by R, which your R will be your payment. So you can use this formula to calculate the present value of an annuity. Those who are using the financial calculator, you do not have to worry about the formula, but you need to know, you need to be able to know what the formula looks like as well. So this is to calculate the present value of an annuity. Otherwise, with your financial calculator, we're still going to use the same steps that we have been using by tearing our calculator, putting in the compounding periods first, on and off, doing the plus or minus. If we are giving the present value, putting the present value, if we're giving the payment, putting the payment, and then calculating whatever we want to calculate, including also capturing your interest and your period, and then computing either the present value or the future value or the payment, or even you can even compute your interest or the period depending on what you are given. So the steps are almost exactly the same. Nothing changes. So let's get an example. If we need to calculate the present value of an annuity of 1600 payments made quarterly for five years at an interest rate of 20% per annum compounded quarterly. Now we need to first understand what we are given in the question. And what is the question asking us to do? So we can see from here it says we need to calculate the present value of a payment made, which the payment, which is our R. So we need to calculate the present value. So we need to find P. If we are given the payment, which is our R, for five years, which is our N, at an interest of 20%. And remember, if we're going to be calculating this manually, we are going to divide by 100. So this will be 0.2, which is our I or our rate. And we are also, what are we given? Compounding periods. And because it's quarterly, how many compounding periods are quarterly? What is our compounding period? Just wanted to check if you guys are able to hear me. Nobody is talking to me. Okay. Candy says it's four years. Compounding periods. Therefore, you need to keep on talking to me because I can't get the chat as well. So then I can also know that people are behind the presentation because I'm not seeing you guys. So they are four. So now we know. And then we also need to identify the formula that we need to be using to calculate. So and that is the formula that we're going to be calculating the present value of our annuity. And we substitute the values. Always remember, your interest is divided by the compounding periods. That's the other thing that you always need to remember. When we answer questions and they are compounded, the interest and the periods is going to be multiplied, whereas the interest is divided by the compounding period. So our interest of 0.2 divided by the compounding periods, which are four. And our period n multiplied by four because the compounding periods were four. And we just substitute the values onto the formula and calculate. So removing them, everything that is inside the bracket, doing the division first, and we get the answer of 0.05 for 0.2 divided by four. And then we simplify it further and then we get the answer of 19,939.35. And that's how you will calculate the present value of an annuity. Any question? Any comment? Is everything clear? Yes, it's clear. Are you good? Yes. So let's look at the same step if we have our financial calculator. So using your financial calculator, it's the same thing. So you will be given the statement to both those with no financial calculator will use formulas. With the financial calculator, you just need to also follow the same. Identify what the question is asking you. The question is asking us to calculate the present value. So therefore, it's asking us to calculate PV, which is the present value. What else are we given in the question? We are told that 1,600 is our payment. Therefore, it is PMT. So on our calculator, there is now we can introduce this. We're still going to work on those functions. Those functions are very important and we're going to work on second function on and off in the mode. And what else? ENT and the number buttons. Those are the only things that we're going to be working on. So let's see. And nothing else. So we know that now we're introducing PMT, which is payment. And our five years is N. And the interest is I slash Y. Our compounding periods, which is P slash Y, which is equals to four. Now, because we're using the steps, you first need to write the steps down before you can even start typing on your calculator or pressing buttons on your calculator. So let's write the steps down. We know that we first need to clear our calculator by pressing second function in the mode. So we need to go second function mode, which is second function CA. And then we capture there. Then we're going to capture the compounding periods by pressing second function P and Y, which is on the I and Y, we press the slash I slash Y. And we put in four because there are four compounding periods. That's why we write the four. And then we press the ENT button. Now we can go and press the on and off button. Because now we start on the memory of the calculator, the compounding periods. To start capturing the data, let's start with the payment. We first need, oh, I forgot about the plus or minus. We first need to press the plus or minus. So you'll say plus or minus 1600. And then you're going to press, press, sorry, payment, because that is the payment. So you're going to say plus or minus 1600 PMT. Because this is the payment given. Then you go and put in the period. Now you're going to say five, second function, and then you press N, and then you press N again. The first time when we press N, we're multiplying with the compounding periods because we're calling this function at the top, which is written in orange. The first time, you say five, second function, N, by calling the compounding periods. So we multiply our period N, five years, multiplied by the compounding period. But we also need to store that value by pressing N again. So you will say five, second function, N, N again. So this is the same as remembering N, N again. So N, N, you will press N twice. And once you are done, you can put in the interest, which is 20. Remember, on your calculator, the value as you see them, you put them on your calculator as you see them. So it will be 20 and you press the I and Y. Then we are ready to calculate the present value. So you will press Comp, PV, Comp, PV. And that will give you your present value, which is your discounted value at the beginning of the 10. That is your present value, your sum of all the payments at the beginning of the 10. That is easy and straightforward. As you can see, the steps looks exactly the same for the calculator, whether you are asking or calculating questions relating to present value and future value for compounding periods or you're doing for payment. The only thing is PMT. Remember, if you are given the present value and you are asked to calculate payment, the first value you capture after you do your on and off, especially if it's payment future value or present value, you need to first put the plus or minus. If you don't put the plus or minus, your calculator will give you a negative answer. You need to be very careful on that. So only the first number, whether it's present value, future value, or present value or payment, you need to press plus or minus first for the first one. So if in the question they give you payment and present value and they want you to calculate the interest, one of them either payment or present value will have a plus or minus in front of them. Okay, now it's time for the exercise. What is the present value of an annuity of 1,500 payable at the end of six months period for two years if money is worth 8% compounded semi-annually? We can do this one together, but you will have to do the calculations. So the question is asking us to calculate the present value. So it means we need to find PV or P. What are we giving? The payment because it's payable at the end of each six months. This is additional information, but it's the same as semi-annual, right? Six months, you must know what six months mean in terms of compounding periods. So this is our payment. This is our end. This is our interest compounded semi-annually or six months. So what is our compounding periods? How many compounding periods will they be? Two. There will be two. So knowing that here is the formula for those who want to use the formula or who don't have a financial calculator, please calculate the present value. I'm also going to put the steps for those who are using financial calculator. So remember, you need to write the steps first before you start calculating. Second function, let's do that. Second function, C A, we always want to clear our calculator. Second function, P slash Y, which is on the I and Y, and then you're going to put in your compounding periods, and then you're going to press E and T. Then you're going to go on and off your calculator, and you're going to press plus or minus. I'm leaving the blanks because I want you to put in the actual value because then you will be able to tell me what values are in there. And this is your payment because that's what they have given you. And eight. Why am I giving you the answer? Let me not give you eight. Let me give you a block. And because I started with that one, I'm going to change it. Second function, and I'm going to press the N N again. And I'm going to press the put the the block. And I'm going to press the I and Y. And I'm going to ask you to come. And that will be the present value. So those who are calculating manually, I just want to get some of the values here, right? We know that our R is 1500. We know that our N is two times the compounding period of two, which is equals to four. Therefore, it means there will be four payments made within that two years. And our I is 0, 0, 8 divided by two, which will be 0, 0, 0, 4. 0, 0, 4. So you just use those values to substitute into your formula. Okay. And then you can tell me which one is the correct answer. I'm going to go to the chat to look at your responses. The other thing is that my battery is on 20 percent and my house is dark. Let's see if I can increase the brightness on the laptop. It is 100 percent my battery on the laptop. I'm good. You can still go on and see. I won't be able to see you on the calculator when I calculate because the numbers are not visible. My screen is dark. Okay. Anyway, while you're still busy, I'm going to go look if I have a candle. Okay. No, it's fine. I was using the daylight now. It's becoming darker outside. So I'm going to look for a candle. I'll be back just wait. Okay. Stop singing. No matches. If this one doesn't work, it's not going to work. It's only one stick. Okay. It's working. I'm back. Now I'm able to see my screen. Okay. Can continue. I see here we have two, two, two as an option. So how do we answer the question? We'll start with the calculator one. Do you want me to tell you? Yes. You can tell me the the values and then I will put the numbers. So the first second function Py, what do we put here? Two. Then E and T on and off plus or minus? One five. One thousand five hundred. That will be our P and T and two here. So I can function N and again and I and Y. Eight. We put eight. Then when you press com, PV, you get? Five four four four comma eight four. There we go. So those work out later manually so that we don't leave you behind as well. So it will be P is equals to one thousand five hundred times one plus our interest of zero comma zero four. I like waking them out first before I substitute into the formula so that then my calculations are clean and it saves time. Four minus one, everything zero point zero four times one plus zero point zero four to the power four. And I'm going to guess that if you calculate this on your case, your calculator that you are using, let's see if I'm able to get to my case, you still don't have a license for it. I still renew my license for the case. So do you also get five thousand? So I'm going to assume that you also get five thousand four hundred and forty four point eight four. Okay. Any questions? No. It was clear, right? Okay. So that was the present value of an annuity. Sometimes you need to calculate the future value because they're not only going to be interested in the present value, but they need you to calculate also the future value. So in order to calculate the future value we use S which is the future value is given by your R which is your payment times the accumulation factor which will be one plus your interest to the power n minus one divided by your interest. That is the simplest formula. Okay. So in order for you to calculate that, let's look at an example. Jack will need to pay twenty thousand to buy his brother's car in two years time. He wants to start saving part of his weekly salary into the account that will retain 8.5 interest per annum compounded weekly. Calculate the minimum weekly payment that he needs to make into the investment account to have enough money in two years time. So we need to understand what is the question asking us? What do they want as calculate the minimum weekly payment? That is what they are asking us. So they are asking us to calculate R or PMT. That's what they are asking. Now what have they gave us? What is it that they gave us that will help us to answer that question? We need to street the sentences again. Jack will need twenty thousand to buy his brother's car. So he will need that. That's what you need in future. So that will be your future value, right? In two years time, that is our period or our time n. So this is our future value. That is our period. He wants to start saving part of his salary on a weekly basis into the return that gives 8.5, which means this is our interest, right? Which will be if I'm going to use my financial calculator, it's 8.5. If I'm not going to use my financial calculator, it will be 0.085. Remember to keep all of it. So I'm also going to do this too, because later on I want to multiply. And they say it is compounded weekly. What are the compounding periods? 52. That will be 52 weeks. Let's see if I have the formula. So if this is our formula, then we just substitute into the formula. So it's 0.085. 0.085 divided by 52, which is our i. So when you do the calculation, do this outside of the formula. Just come here and substitute into this the actual value. So I'm just demonstrating here that you need to divide your interest by the compounding period of 52. And you need to also multiply your period by the compounding period of 52. So you substitute into the formula. Now we're not given r because r is what we need to be calculating, right? That's what they're asking us. We are given the future value, which is your s, which is 20,000. And then we just divide the accumulation factor with the 20,000. After you have simplified, you will just divide the answer you get for the bracket. 20,000 divided by that answer. And the answer was 113.23 and some numbers. And when you divide that, you get 176.58. So in two years, he needs to make 176 cents and 176.58 cents weekly payment in order to get to 20,000. That's what Jack needs. If I'm using a financial calculator, the steps are the same. Yeah, your calculator from any stored value put in the compounding period on and off your calculator. Put the present or the future value because that's what we have. We are given the future value put in the interest and your period. Remember all these three steps, all of them. There is no order that says you first need to do future value first. You can even start with the interest and the period. Then the last thing you do is put in the future value. So you can interchange them. Doesn't say these are the steps stick to them, but you need to make sure that you have all three of them. At least three of the values kept check before you compute whatever you are asked to compute. So yeah, we were asked to compute the weekly payment. And when you press compute, the answer should give you 176.38. Okay, and that is a new it is for future value and present value done. Now we can go into doing more exercises. 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% of the compounded monthly. So what will be that lump sum that is required? I'm going to give you two minutes to think about it to do it to try it. Five minutes actually, let's say five minutes. And then we will come back. I will ask you how you answer it. But if you have the answer, you can put it on the chat, but we will do some feedback. So your five minutes, that's right now. Are you winning? Are you winning? Yes, we are. You know that on the chat function, when someone posts something, you are able to use the emojis. So I'm tempted to use an emoji on the answer that I already see on the on the chat. Let me see if there are no nice other emojis again. It's only those ones. And whether should I say, I'm laughing, I'm surprised. I'm sad. Or should I say I'm angry here? Angry is very worse. I'm joking. All right. I'm still waking up. And this also says three. If there was an emoji called, ha. If you surprised me, let me use surprise to surprise. Because I think that is the closest one to aha. I'm very unsure of myself because I don't know if I'm doing future value or present value. The only emoji I can put for your two responses there is ah. So there's no ah. They are surprised. Are you still calculating? Let us not distribute. You will notice that I'm not loving it or I'm not liking it. I'm saying ah. That means go and read the question again. I'm joking. But yes, go and read the question. It's a very tricky question. Okay. How is everybody doing now? It is almost more than five minutes. Struggling a bit. Are you using a financial calculator or are you calculating manual? Manual. Okay. Let's save everyone some time before they even continue. So let's read the question and then you will tell me. Sorry. Find the lump sum that one must invest in an annuity, right? Find a lump sum that one must invest in an annuity in order to receive a thousand at the end of each month for the next 16 years. If the annuity pays 9000 compounded monthly, the lump sum that one must invest in in an annuity in order to receive one thousand at the end of each month for the next 16 years. If the annuity pays 9% compounded monthly, is this what they're asking us? Are we calculating a present value or a future value of an annuity? It's a future value. I don't know. I'm being honest. I don't know. I'm unsure. I thought it was future value first and then I said no, it must be present value because you must invest it before you get five months. If the annuity pays 9% compounded monthly, remember that is a thousand at each of every month for the next 16 years, right? Yes. So, order for the annuity to pay a thousand every month, how much you need to be investing for the next how much lump sum you will have or how much lump sum you need to invest in an annuity in order to receive a thousand. So, it's like the question is like asking you to go backwards. It's a very tricky one. You might interpret it as find the lump sum that one must invest in an annuity because then if I invest 102 and it pays a thousand every month for the next 16 years, but that is not the money you're going to be receiving. However, if I have saved an annuity will be able to pay me a thousand run in the next 16 years, if that annuity has accumulated interest of 9% monthly. So, therefore it means you need to be calculating the future value of that or the present value, the future value of that because once you have invested, you've got saved up money and for 16 years you will be receiving a thousand. So, the question is asking you to calculate the future value, isn't it? That's correct. So, if it's asking us to calculate the future value, then we need to calculate second function CA, second function P slash Y, our compounding periods will be 12 because it's monthly and then you press E and T and then you go on and off your calculator plus or minus our present. So, we're given the payment because that's what you're going to be receiving every now and then, a thousand which is your payment, your interest is nine, I and Y, what else? The period 16, second function and and again and this is how much you should have in your annuity. In order to receive that, that is your future value should be that much and what will be that future value that you have that will give you a 10 every month for 16 years that will allow you to get a thousand rent every month with interest of 9%. If you calculate that, you should get the answer date. I don't know what answer will that be. So, if we're using the future value here, then it's r times 1 plus i to the power n minus 1 divided by i. So, also that will be a thousand. So, your r will be a thousand, your i will be 0,09 divided by 12, your n will be 16 multiplied by 12 and that will be the values that we substitute onto the perfect calculator, what is 0.09 divided by 12, 0.0, 0.0, 0.075 and what is your period? It is 12 multiplied by 16. There will be how many payments you will receive in 16 years? 192 payments. 192 payments in the next 16 years that you will receive and that will be 1 plus our interest of 0.075 to the power of 192 minus 1 divided by 0.0075 and if you calculate that, you should get the same answer as the others. So, what do you get? Let's see, because you guys, you don't want to talk to me, so the other one says it's number four. Lizzie, I'm sorry, I'm having a network issues. I also have a network issues. Are you able to hear me? How did you get the lump sum to invest? Isn't that the money that you need to invest? On the day you get 1,000 bucks for 16 years, but how do you invest a future amount? Remember, this will be the amount that allows you to receive 1,000 at the end of each month. It's not the amount that you need to be saving. This is not the payment that you need to be making every month in order to receive the future value. So, this is the future value. This is the 1,000 that you will receive from the amount you would have saved. So, if you use the present value, remember present value, you need to be making both payments on it, isn't it? The metric is an issue now. I've got the 1,000, the 1,000 right is the payment that you received, but from what amount? Because you need to put something in for you to receive. Oh, am I getting it wrong? I'm confused now. Among the same pages, I think the same thing. I think you need to work out your present value because your money earns interest over the 16 years that's in there as well. Remember now, wait, wait, wait, wait, wait. Remember now, you thinking about the compounding interest here, it's asking you what will be that amount that allows you that in the next 16 years, you will receive 1,000 rent at the end of each month. In the next 16 years, what will be that amount? Now, this is like if you have a savings account, how much will that saving pay you every month for 16 years? That's what it's saying. It's not about how much money you need to put in in order for you to receive a lump sum at the end of 16 years, right? Read the question. In order to receive each month for the next 16 years, so how much you will be having payments given to you, not payments you are saving or saving, how much money you will have in order to allow you to receive more 1,000 rent every month with interest of 9% compounded monthly. So you need to have some money that it's going to yes, it's going to allow you at the end for 16 years to receive 1,000 with interest of 9%. And that is not 101, that won't give you that because that would be the future present value if you are going to be making payments, if you are going to put money into that, then that will be there. But this one says if you're going to be receiving the 1,000 for the next 16 years. That is why the trick about this question comes in. So you need to read the question and show that you understand what they are asking you. So let's go back to here. I need to buy this much. I need to make a payment every week of this much. That's what we calculated we said. Oh, not this one. It was the other one. So in order for me to get that, which is my future value then, I need to be making payment of this. Back to the other one was the present value. So in order for us, which one was the present? In order for me, if I'm going to be making a payment of 1,500 for the next two years, this will be my present value. This will be my value at the beginning in two years with interest of eight. So when I start at the beginning, I will be putting 1,500. That is the present value at the beginning. The future value will be if I put the same, but remember this one is discounted. It will be discounted. Interest will be discounted. That is why at the bottom here, we divide by the interest times the accumulation factor of that 1 plus i n. It makes a huge difference that the thing that you are dividing by. So you will notice that if you take the same amount and you use your future value, your value here will be more than that, because that will be the lump sum at the end. This is the lump sum at the beginning. Now, the lump sum at the beginning is different to the lump sum at the end, because now the two questions are totally different. The one question that we are on, it says the amount needs to allow you to receive money. It's like if I'm banking, I'm banking, I'm banking, and then at the end I've got this money. If I take out a thousand every month for the next 16 days, how much should I have in this future value account that I have? Not this, because if I have money here, then I'm still going to add until I get to the future. So yeah, it says if I have this money, which is in the future of this amount, how much it will allow me to take out a thousand every month? For the next 16 years, no. Okay, I get the question now. Thank you very much. All right, for the next 60 years, and it says you receive an annuity. It's not like you're making a payment. You are going to be withdrawing. This is where we draw out. Okay, so and that will calculate the future value, and that's the formula that I wanted to share, but I wrote on top of it. But that is the formula you will use. Okay, so we can continue with the exercises. So it means also, you need to pay attention when you read the questions. Not everything as you see for the first time. Remember, you need to make sure that you understand what exactly are they asking you. And what kind of information have they provided you in order to help you answer your question? That is very important to identify. Okay, so let's read the next one. Maybe this one will be as easy as possible. A farmer needs 250,000 to purchase a 10 ton trailer. The bank approves the loan for the full amount. The interest rate is 18% per year compounded monthly. The loan has to be paid off in five years time. Determine the farmer's minimum monthly payment. The farmer needs 250,000 to purchase the loan. The bank approves the full amount. Determine the rate at 18% per year. Compounded monthly, and the loan has to be paid off in five years time. Determine the farmer's minimum monthly payment. What is it that we are giving here? Is it the present value or the future value? Before you even start calculating. What is this 250,000? Present value. That will be your present value. So now, when it comes to annuities, always remember that savings are future. That's the other thing that I also need to raise with you. So mostly savings always warrants for the future value. Loan is your present value. If you get questions where they talk about savings, it means probably they're talking about because at the beginning, you don't have anything. If you're not putting in a deposit, you don't have anything because it's saving. So you're going to accumulate money and have a future value. That is saving. A loan, a bank gives you the money. When they give you the money, that is the money you have and you need to pay it back. So that is your present value that you have, but you need to make payments to pay it back so that you can end up having a zero amount. Whereas with saving, you're going to have an accumulated amount at the end of that period. So you always need to think about it in this way as well. Okay. So we know that we are given the present value. What else are we given in this question? The interest of 18% compounding periods, there will be 12. The loan has to be paid in five years. Which is the period. So you can continue and do your calculations. So because we're using the present value of an annuity, I'm going to put it there. So we know that our P is 250,000. Our interest is 0.18 divide by the compounding periods, which are 12. Our N, which is 5 times 12. And you can find the answer. And then you're going to use P is equals to R times 1 plus i to the power N minus 1 divide by i times 1 plus i to the power N. That's the formula you're going to be using. Second function, CA, you're going to write those who are using financial calculator. Second function, P slash Y. And then you put in your compounding period and you press ENT. We go on and off. And okay, this one you need to put the plus or minus first. Plus or minus. And you're going to press or put in your present value. And you're going to press the value of your interest. And you're going to put in the value of your period. By pressing second function, N, N again, N comp, P, M, T. What is 0.18 divide by 12? 0.18 divide by 12 is 0 comma 015. 0 comma 015. So you just substitute it and 5 times 12. I think it's 65 times 12. That should be 60. Sorry. Those who are calculating using manual calculators, it might take you longer. Otherwise, you just substitute and use your cashier. The answer is 3 for present value for future value. In the exam, you just need to choose one. Okay, Candice, your answer is it for this question that we are answering now. Yes. Okay, thank you. Let's see. Come on. Sorry. Are we winning? Okay. So if I substitute the values, I know that my present value is 250,000. My rate, my payment R is what I'm looking for. Then it will be 1 plus I of 0 comma 015 to the power of 60 minus 1 divide by 0.015 times 1 plus 0.015 to the power 60 and therefore it means the answer I will have is R is equals to 250,000 because I just need to take the thing in the bracket divide by 250,000 and that will be 1.015 to the power of 60 minus 1 because I don't, I'm not going to calculate it as yet. 0 comma 015 times 1 comma 015 to the power 60 and the answer you get here should be somewhere in the region of 6348.36. Let's see. On the other side, your compounding periods will be 12. You must let me know if you're not getting the right, the answers as me. Maybe I made a mistake somewhere. The plus or minus our present value of 250,000. Am I still on the right track? Our interest is 18 and our periods is 5. So just double check your steps and double check your values and see if we have the same answers. So the answer here will be option 4. Is that right? Okay. Let's see if we can squeeze in another another question. Cherry wants to take her family to a vacation in two years time. Suppose she deposits 192.86 in the beginning of every week into the account earning 9.2 interest compounded weekly. Determine the amount she will have in two years. What are they asking you to calculate? Future value. Future value. They're asking you to calculate future value or S. What are you given? You just need to identify the values that are given in there. Let's go and identify them. I will start with the manual one. Am I given the payment R? Yes, which is 192.86. I'm given interest, which is 192. So it will be 0.092 divided by my compounding periods. There are 52 weeks. So you just go and calculate that. You will give me the answer once you're done. And they said the vacation will take two years. So in two years time, they need to go on a vacation. So it means the period in two years that she will have this money as well. Our N will be two times 52 weeks. And you can give me the answer for those two. So what is 0.922 divided by 52? Those who are calculating manually. Okay, while you're still calculating that, so let's go and put in the formula as well so that you can continue while I write the steps for the calculator one. So because this is a future value, we use 1 plus I to the power N minus 1 divided by I. So you use that formula. So go and calculate the other values and substitute. I will be with you just now. Those calculating with the financial calculator, so I can function CA. I can function P slash Y. Go and find out what your compounding periods are and then press E and T on and off your calculator plus or minus. What are we giving? We are giving the payment. So therefore it means that's the way we're going to catch up our interest, which will be I slash Y, our value of the periods, which will be second function N and again second function and the first time multiplied by the compounding periods and then restoring the value. And the last step, COMP FV. As you can see that the steps are almost exactly the same. You just repeat the steps. By the time you go write the exam, you feel comfortable. You don't even have to write the steps down. You will just be taking your calculator and then going through the steps. But it requires you to practice. They say practice makes perfect. So you need to practice and practice and practice. So ladies and gentlemen, do you have the answer for I? 0.0018 Because our calculators are stored at two decimals. Let me see if I increase the decimals. Of course let's do six. Let's remember that we need to keep all the decimals, right? Interest exactly. So if I keep all the decimals, I get 0 comma 0, 0, 1, 8, 4, 0. It's very difficult to write all these numbers. Let's write the formula small. 0 comma 0, 0. I go on top of one another. 0, 1, 8, 4, 0, off. Okay. And 52 times 2 is 104. So we can just substitute. We're looking for the future value. We are given 192.86 times 1 plus 0, 0, 0, 0, 1, 8, 4 to the power 104 minus 1 divide by 0 comma 0, 0, 1, 8, 4. Those were calculating. I hope you have your steps right. That is 52. That will be 192.86. This will be 9.2 and this will be two years. What is the answer? Let's see. The chat is flicking. Convay, is that the answer for now or for the previous? Okay. I see Candice responded twice. So the answer is four. Is that what you're saying? Yes. Do you all get option four, brothers? Okay. So the answer will be option four. Okay. It is 7.18, so we still have little time to include another exercise. Siamo wants to buy a franchise that costs 250,000. He is planning on using 150,000 of his savings and take a loan of the outstanding amount. The loan has to be paid in five years' time and in monthly payments at a fixed interest rate of 17.5 per compounded monthly. How much will Siamo pay on a monthly basis? That is the annuity question we are asked. So what are we given? Sorry, Lazi. Are we attending to the immortalization? No. Last week. I came in late so. Nope. This is still payment. We're still talking about annuities. Amortization is next week. Okay. Remember annuities are payments, right? Yes. And we use annuities to do amortization at the later stage, but especially with the present value of an annuity. But today we're talking payments. So what are we given? We know that we need to be calculating payment because that's what they say. How much they will have to pay on a monthly basis? What is our present value or our future value in this instance? What are we given? We are calculating present value over 100,000 because it's 250 minus 150,000. Present value of 250,000 minus the 150,000. That will give us the 100,000 because we need to because they say only he's only going to take out a loan of the outstanding amount and he's using 150,000 from his own savings. So there is our present value. You also need to identify what other things you are given. So we know that it's for five years and we know what the interest is and we know what it's compounded monthly. So we can go and start with this. Our P is 100,000. Our I is 0,175 divided by 12. Our N is 5 times 12, which is 60 and we can just then calculate our present value of an annuity of R times 100 plus I to the power N minus 1 divided by I times 1 plus I to the power N. Now, you can also write it this way or you can write it like R is equals to P divided by your accumulation factor 1 plus I to the power N minus 1 divided by I times 1 plus I to the power N. It will give you one and the same thing, the two formulas. Second function CA, second function P slash Y put in the compounding periods ENT on and off your calculator plus or minus the value given as your present value, the value, second function N and again the value I and Y, which is your interest and then your comp PMT. So we can do it as a competition. Let's see who gets it first. Those with financial calculate and those with manual calculators. Okay. Are you using a financial calculate? Yes, financial calculators are quick, but also those who are using the manual calculator, you should be able to get it quicker because you will use your cashier calculators to put in the fraction thing and then it will calculate your answer. So one plus we still need the value of our I. What is I? Point 175 divided by 12. It's a very long number, a very, very long one. So I'm just going to keep one, two, three, four, five, six. I'm going to keep six digits. It's interest if you want to get your answers right. You need to make sure that you keep all your digits when you are still calculating. So in this instance, on your fraction calculator, you can do fractions on the so that you don't lose the digits. This is zero comma zero, one, four, five, eight, three plus some numbers. I'm not keeping all of them. I'm just going to keep some of them. Anyway, I'm not even going to bother to substitute. You do it on your side and then you get me the answer because the numbers are very long. Otherwise, I can just do 100,000 divide by one plus zero comma one, seven, five, divide by 12 to the power of 60 minus one, divide by zero comma one, seven, five, divide by 12 times one plus zero comma one, seven, five, divide by 12 to the power of 60. And that should give you your answer. And this side, double check your statement if you have the same values. Our period, it's five. Our interest, 17.5. Easy, right? Should be easy. So next month, when you write your exam, those who are doing QMI, it should be easy to sail through the questions. Okay, we left with four minutes. So in the next four minutes, I'm just going to recap and go through some of the exercises that are included in the handout. The handout, remember, the app had off. The notes have already uploaded them, so they are there. You can go through them. So we do have a question on the business woman who wants to invest the same sum of money at the end of each quota for 5,000. And in order to accumulate the total of 80,000, at the end of five years, what is a required quarterly investment? So you need to look at the question, find what the question is asking you to calculate, identify what is given in the question, and answer that. Always remember that loan, mostly it's present value. Savings, it's mostly future value. If you can always remember that, when you read questions, you will automatically see things come together, because then you will know that this question is asking me to calculate future value and this one is asking me to calculate present value. I'm sorry. My numbering on these things are not right, so I start from four and then I go to three. Okay, so there is number three exercise, which is number five in a week. Also, yeah, they give you information. Please identify what you are given and what you need, what you need to be calculating, because yeah, they say what is the amount that they borrow or they borrowed if they have to make that. So don't assume that because they give you monthly payment, then assume that this is future present value or this is future value. You need to read the statement and make sure that you understand, and based on the things that I just told you, known present value. Savings, future value. Future value. Yeah, and the last one, so like I can see that I'm going from four downwards. So this is exercise two, which should be exercise six probably, and also identify what is given in this question and answer the question that's on, that is on. And I think this is one of those that are almost like similar to the previous one, but it's not, but it's one of the other questions. So you are given the loan, you make it down payment. And you might notice that this question, we might also do an amortization because I think I took some of the question from amortization into year because in your exam most of the time, your annuity questions and amortization questions, they are almost asked in the same question. Like for example, they will give you the statement and that statement will relate to question number 23 and question number 24 and question number 25. So you always need to make sure that you work through it because annuities are part of amortization. Okay, so we come to the end of the session. So far you have learned how to do some basic calculations when it comes to annuities, how to calculate the future value of an annuity, and how to calculate the present value of an annuity. Remember that annuities are payments made on a regular basis or subsequently or successfully, like one after the other. If it's quarterly, therefore it means the payments are made quarterly. If it's monthly, it means it's monthly. So you always need to remember that the compounding period, you need to divide your interest by the compounding periods and you need to multiply your period by the compounding periods, especially for those ones who are calculating. But if you're using your financial calculator, yeah, the steps are the same whether you're doing future value or present value, the steps remain the same. Read what you are given. Write down the steps. It's very important to write down the steps because you are able quickly to see where you have gone wrong and can fix it and then calculate it. As you are practicing, do that. Don't take shortcuts. Shortcuts won't get you anywhere, especially now, while you're still understanding the content and you are preparing to write your exam. And that is me. Any question? Any comments? Because of the session? We got a mock examination for two hours and I actually got 85 percent. So seeing that we lost us, it helps me because two years back I did this module and then I completely didn't understand. But now, attending your classes, I do. It is my pleasure that at least you see the light at the end of the tunnel and I wish you all the best with your exam. If you're a mock exam, it's a practice mock exam like it gives you opportunities to try and try and try those who are not getting it right. Please do because they say practice makes perfect. It's perfect. Yeah. No, it's the second exam, so you only get one chance. So your lecture only gives you one chance. They are not free. They should give you at least two chances because it's a mock exam. It's a mock. So they must open it up to give you two chances. The first chance is to see if you are comfortable with doing the exam and then you do it again. It's practice. Mock exams are like practice activities. I hope that they give you those questions as a print out maybe as a PDF so that you can practice because I understand the concept why they would want you to take a mock exam. That resembles an exam because they give you some practice so that when you get to the exam, you are able to time yourself because it's about timing. You are able to time yourself and making sure that you move with the correct space like speed when you answer in your questions so that you don't, the time doesn't lapse while you're still busy doing the work and it also gives you some practice so that when you go to the exam, it's not something that you see for the first time because I'm going to assume that your assignments are hard copy assignments but you have to do them online. Whereas with the exam, you will never get a hard copy. Everything is online so it means the screen time plus that you don't get the time to play around then online. Usually the time moves faster than when you're writing a paper on paper. Okay so someone was asking for was was requesting a sorry month to interrupt what you call it register attendance. Oh the register let me see if I can paste it if it's still in my memory yes it's still in the message. I have just posted it and please make sure that you complete the register. Thank you. Yeah so I will see you next week when we discuss amortization. So those without the financial calculator, I hope by the time you go write the exam you have your financial calculator. You don't want to lose marks because I think I knew it is there you might get that there are about two or three or four questions asking you about amortizations and they are very tricky the amortization questions. Like I said it includes calculating your present new your payment. It will include calculating either the interest or the outstanding balance or the total and then they might ask you as well change if the payment is no longer this what will be that. So it's very very tricky if you don't have your financial calculator you don't want to lose marks for that. If you are able to pay 800 rand or plus or minus because they're expensive other other other places