 So yes, welcome to another session of basic numeracy schools, where we learn the skills to solve your BNU and QMI module conflict. So today we're going to discuss simple interest and compound interest, since we only have one hour 30 minutes, has the recording started, I didn't check, sorry, I have to go double check. It is recorded. Yes, like I said, we're going to be discussing simple interest and compound interest. And if time allows, then we will have lots of other activities because I've included more activities on a later stage. Okay, before we start with today's session, do you have any questions going once, going twice, and it's gone. Okay, in the absence of questions or comments, we can then look at simple interest and compound interest. Now this, for today's session, I'm going to show you how to use your calculator. Those who have a financial calculator, the financial functions, the financial math function, we're only going to use them when we get to the compound, when we calculate compounding periods. And when we do annuities and amortization, the calculator will come in handy. If you do not have a financial calculator and you are planning to buy a financial calculator, I will suggest that you do that as soon as possible. Do not wait a week before you write the exam and think that you are going to practice with your financial calculator and know how to use it there. You need to start now. So if it means you have at least 800, because that's how much that financial calculator costs, go and buy it right now. You can make sure that this week, the next three weeks, you no longer eat takeaways. You budget that money for takeaways or taking the kids out or doing some fun things. You say, hold on, I need to pass BNU or QMI. I need to invest in this calculator and go and buy that. But for now, with simple interest, we are just going to use your normal functions on your calculator, like a normal calculator, to answer the questions. So what is simple interest and what is discount? By the end of the session, for now, you should learn how to do basic calculations if you get questions relating to simple interest or simple discount. A simple interest is interest you pay when you buy or when you borrow or when you invest. When you save money or borrow money, then you pay interest on it. That will be your simple interest. You only pay it once off at the beginning of the day. So it gets calculated at that point. It is calculated as a fraction of the amount you are borrowing. So remember, at some point, we did percentages. We did calculate what is the percentage of a number. So with interest as well, it is that proportion or the fraction of that whole intent in relation to that percentage or that interest. And your interest will be in percentage. And when we use it, we're going to divide by 100 so that we are able to use it in a decimal format. And because when you borrow something, you borrow it for a period of time, so also the interest will be calculated based on that period that you are taking the money for. Like I said, it is payable at the beginning of the term. And interest because it's an amount. Remember, an interest is an amount and an interest rate is that percentage or that fraction or the proportion that you're going to use to calculate how much. So in terms of interest, the formula we use is I that represents interest. It's given by your principal amount or your present value times the rate, which is the interest rate, times the time or the period, which is the how long you're taking out or you're saving that money for. So it's I is equals to PRT, which is easy and straightforward. If I want to calculate the future value of that interest, then the formula will be your principal amount plus your interest. Already, we have defined what our interest is in terms of symbols. Future value is S. Our principal, we're going to use P and our interest, we're going to use I. But we have already defined what I is. We said I is PRT. So if I replace I with PRT, then the formula changes and becomes S equals to P plus PRT, which is principal plus interest. However, in math, we can summarize this by taking the common factor. I know that we didn't deal about the common factor because we have gotten that part when you rewatch some of the videos from last semester as well. So a common factor is the value that both of them look almost exactly the same. So P and P exists in the plus and the plus PRT. There is a P, which is a common factor. If I take it out, if I take it out, then I will be left with one where P is because if I take out P, I'll be left with one. And if I take out P from PRT, I will be left with only one times PRT, also one times RT, which is the same as RT. And the formula that you're going to use and you need to know it is just as simple as that. The future value of a simple interest is given by your principal amount times your accumulation factor, which is one plus RT. Let's look at an example. If you borrow an amount of 7,500 at an interest rate of 15% per annum or per year, what will you have to pay back if the repayment of the loan is within format? Now, the other thing I need to bring to your attention is that when we calculate interest or compound because your interest is per year, so we always use per annum or per year. So it means everything, including how long we will always into the default mode will be a year. It will be a year. So if that is the case, then it means our time that we need to always use needs to be always be converted to a full year. For example, here we have four months. So we need to convert this to a year. We cannot work with four months. We'll have to convert it to a year and to convert a value to a year. The same thing as when you convert a minute to an hour, you divide by 60 seconds or 60 seconds. So we do the same. You multiply by 60 seconds, one of the two. So in order for us to convert four months, we need to get it to a year. So therefore, we will say four divided by 12. And that should give us what we are looking for. I'm not going to do that as yet. So but now let's understand what the question is, what they have given us. So with relation to the question given, let's identify. Or we know that the question is asking us, what will you have to pay back? Therefore, it means they are asking us to calculate S. That's what the question is asking. What are the facts given? The first one is our present value. The second one is our interest rate and our interest rate is R. And we know that we need to divide it by 100. So it will be 0,15. And the next one, they told us how long we are taking it. And that should be our T. But also, we must remember that our T, we need to divide it by 12 to get to convert it to a year. OK, so now we can substitute into our formula. And we know our formula is S is equals to P times 1 plus RT. So let's substitute. P is 7500, 1 plus our R is 0,15 times 4 over 12, which is our period, or our time. Solving the equation, 4 over 12 times 0,15 gives us 0,05. 1 plus 0,05 gives us 1,05. Multiply that with 7,500, and the answer we get is 7,875. And that's how straightforward and easy it is to find a simple interest. Now, in this question, actually, there are a couple of things that are not stated, but that are key to how you're going to identify the question in the assignment or in the exam. Here, because I'm using simple interest as an example, I didn't repeat the statement. Usually, your statement will read S. You borrow an amount of 7,500 at simple interest rate of 15% per year. What will you have to pay back? That's how the statement will read, because here I'm just using an example. In the exam, you want to have an example, but they won't tell you which one is which. You need to go into the question and identify those key things, including simple interest rate. And that will guide you in terms of what you need to be calculating. Now, let's move to discount. A simple discount is a process of finding where the present value of a given amount that is due on the future value, and it includes a simple interest. Now, in other words, the discount is an amount by the simple interest process to find what will be your actual present value or what we call it a discounted value. So it is always the difference between the amount, your discount amount, and its present value. So in order for you to find the discounted amount, because the discounted amount also will be a proportion or a fraction of the present value, because you are going to say with how much discount you are giving. And that will give you an amount. And if you take away that amount from the present value, that will give you your actual present value. OK, so a simple discount, which is the amount, is given by your present value times the discount rate times the period. The period is the same as the time for how long you are taking this, but for how long you want to discount it for. Where your D is your discount, let me double check them. A D is a simple discount, a P is your present value or your principal amount, D is a discount rate, also a percentage, and T is the time or the time in the year. Let's look at the next example. This is just the same formula. So to calculate a discounted value, remember a discount is the amount, like simple interest is an amount. So discount is also an amount. So to calculate a discounted value, which is your new present value now, if this is your present value, your new present value will be given by your present value, your previous present value minus the discount amount, and that will give you your actual amount that is discounted. So your discounted amount is given by your present value times one minus the discount rate times the period. So if you would have noticed in terms of the future value, we said it was P times one plus RT. So this is accumulation. This is a difference. So you can see with the plus, you can see there with a minus. So for a discount or a future or a present discounted value, we use P times one minus DT. So Anna borrows 1,200 for 10 months and a discount rate of 15% per Anna. Determine the discount and the discounted principle. Here you can answer this question in two ways or you can answer it in one way. So first we can determine the discount because that's what they asked us, find the discount. That's the first question. What is it that they also gave or asked us? Let's see, based on this, what are the facts? 1,200 is what they borrowed, so that is our present value. 10 months, that's for how long? That is our T. But remember, it will be T divided by 12 because it should be in years. Let me go back because if you look at something, it's wrong with my mouse moving up and down. Sorry about that, sorry, sorry, sorry. So this is our discounted amount, also in the time, and a discount rate of 15%. So we know that this is our D, a small D, which is 0,15 as well, divided by 100. Determine the discount amount, that's what we're going to be using. Let's substitute into the formula. Our P is 1,200. Our D is 15%, which is 0,15. And our T, which is the 10, is 10 over 12. And we calculate, I've got too many, too many close brackets. And when you calculate, you will get the discount of 150 rep. And from here, they say what will be the discounted principle, which is the discounted value. You can say 1,000 or your discounted value will be 1,200 minus our discount of 150. And you will get the answer, which is equals to 1,200 minus 150 is equals to 1,050. That is the second part. That's how you can answer this question as well. Alternatively, to answer the discount principle, you can use the second formula, or that last formula, not the second one, the last one, where it says the discounted value will be equals to your P times 1 minus DT. And if I substitute P, it's 1,200. 1 minus D is 0,15 times 10 over 12. And the answer we get will be the same as just using the first one. So you still get 1,050 in both cases. Here is our next exercise. Now, remember we did changing the subject of the formulas and learning how to manipulate an equation. So this is one of those kind of questions where you will have to manipulate the equation. Because if you read this exercise, it says, Joseph invests 36,000 at a simple interest rate of 6% per annum or per year. How long will it take for Joseph's investment to grow to 55,000 now? What are they asking us to do? They are asking us to calculate how long and how long it's T. So T is multiplying with R, and it is inside the brackets. So it means we need to make T the subject of the formula. So we can do this in two ways. So I'll do both ways so that you can understand how you can solve the same question if you get them in your assignment or in your exam. Step two, what are the facts given that we need to identify? They invest. You must also think when you were keeping with financial meds. You need to think what is a loan and what is saving. So saving, you only get the money at the end. So if I need to save, if I need to save for a car and I require 120,000 rent to deposit for a whatever the car I'm buying. So because I'm only getting the money, then it is my future value. If I am saving an amount, it means I'm getting, if I am, but anyway, I'm going to confuse you right now. But at the moment, we need to remember if you are saving, that is your present value because you are putting in the money. If you're putting in the money, the loan as well, if you are putting or they're giving you the money, that will be your present value. So you need to think about it in two ways. Is the money I'm talking about, is it the money I will only get in the future, then that is the future value. Is the money that I'm talking about, is the money that I'm putting in now, then is the present value. Right. And later on, we will expand on those two topics, on those two, how to identify which is which. So in terms of this, I'm investing, so I'm putting it now. So that will be my present value. And they told us that it is at a simple interest rate, so that will be our R of 0,06 because it's 6%. How long? It's a T and the money needs to grow, therefore it means it needs in future, I will get 55, which is my S, which is the future value. Now, I know what formula I need to use because the statement said simple interest. It's very important to identify what type of interest you are calculating. Later on, you will see that there are two different, therefore you need to use a different formula. So for simple interest, we use S is equals to P times 1 plus RT. So since our formula looks like this, the first way you can do is to convert your formula before you do your substitution. Let's convert our formula. So let's take our formula. We know that S, if we want to make T the subject of the formula, we can divide this side by P, so therefore we divide this side by P, divide that side by P. P and P will cancel on one side and you will be left with 1 plus RT and on the other side, you will have S over RT, S over P is equals to 1 plus RT. Now, we need to get rid of 1. We still want to leave T on its own, so the first thing we need to do is take away this 1. So to take away 1, we're going to say S divided by P because it's positive when it moves over, it will be negative and you will be left with RT. Now, from here, you can swap them around because they are equal. This side is equals to the other. I can rewrite this as RT is equals to S over P minus 1. If I want to get rid of R over T, I can remember how do we get rid of R? We can divide this side by R, therefore it means we need to divide this side by R. Or you can say we multiply this side by 1 over R, then we also going to multiply this side by 1 over R. And when I multiply this side by 1 over R, R and R will cancel and you will be left with T on this side and you will be left with S over P minus 1. Times 1 over R. Otherwise you can also divide everything here by R, you can divide by R. So if I divide this side by, because 1 times everything in the bracket will just be that. So the answer here you can say is T over S over P minus 1 times divide by R. You can rewrite it that way. They will give you one more or less the same answer, those two. And then you can then go ahead and substitute the value. So let's go and use our formula to substitute. So we have T is equals to S over P minus 1 divide by R and our S is 5540 over our P is 36000 minus 1 divide everything by our interest. Which is 0 comma 06 and you can go in and calculate and let's calculate the answer because I'm using my case show I'm going to do everything on at once. So it's 55440 divide by 36000 and maybe I should be sharing my calculator so that you can see what I am doing and the answer I get is 9. 9 yes. That is one way of answering the question. The other way is by using the same formula. So S is equals to P times 1 plus RT. We just substitute the values. So the first one S is 55440 equals our P is 36000 times 1 plus 0.06 T with multiplying by T because T we don't have and you do the same. You divide by 36000 on both sides so this side you will have 55440 divide by 36000 and you will be left with 1 plus 0.06 T. Now we want to remove the one to the other side so we'll be left with 55440 over I'm not even solving it. You can see that I am just manipulating the equation without even getting the answer right T. And now I can put everything into bracket 55440 over 36000 I forgot the 0 there minus 1 equals, sorry before I put the equal because I need to get rid of 0.05, 0.06. I'm going to multiply the site by 1 over 0.06 equals T because I'm getting rid of that 0.05 you can have it that way. Or it's the same thing as T is equals to 55440 over 36000 minus 1 divide by 0.06 whichever way and the answer will also still be equals to 9 because you can see that the same equation that I just used is the same one. Are there any questions? I might be talking Greek or Japanese or a language that you guys don't understand, but that's how you will answer the question in the absence of questions. I don't know if you guys hear me or I'm here alone. I didn't even check. Oh you are all here, you are all here. Okay. So I'm guessing you guys can hear me. I'm not losing you, but you are more than welcome to stop me or ask any question if you have, right, so that I don't just talk, talk, talk, talk, talk and explain, explain, explain. Okay, let's look at another exercise. Tandy signs an agreement to pay 20,015 months from now. The simple discount rate is 12.5% per annum. The discounted amount she receives now is... So what is it that they want us to calculate? The question is asking us to find the discounted amount which is our discounted value. What is it that they have given us? Let's look at the facts given. Tandy signs and agreements to pay a 20,000. So signs and agreements to pay a 20,015 months from now. Okay, I'm going to assume that this will be our present value for now because we're going to discount it. 15 months is in when we, when are we discounting this, 15 months will be 15 divided by 12. Remember, our time needs to be in years. So since they said months, we just convert the month into a year. And we are also told at the simple discount. So it means we already know which formula to use. At the discount rate, our D of 12%, 12.5% is the same as 0,125. The other thing you need to also pay attention to when you work in financial matters is your interest. You keep all the decimal. Do not round off. Do not say that is 12.13. Keep it with all the decimal. If the interest rate was 12.75, you're going to keep all of them. It will be 0,125. Keep them as they are. Never round them off. Okay, so let's calculate our discount amount. So DV because we can just use the, the last one and not the second one because then it means I will do two steps if I use the first one. So we just going to use the second one. DV is equals to P times one minus DT. Our P is 20,001 minus our D. 0.125. Multiply that with how long? Which is 15 divided by 12. Close bracket. And that is equals two. I'm going to open my calculator. Let's hope. It's not going to give me issues. Usually, if I haven't used it the whole day, it stopped working and I have to go and activate it. It is not going to work. So before I share my entire screen. Let's need to activate that. So let me share my entire screen so that when I do use a calculator, you are able to see what I am doing. Let's answer this question. 22,000 times open bracket. 1 minus 125 open bracket option. Sorry, I need to get my calculator back to meds function. 1 minus open bracket. Not yet. 0.125. Open bracket function. 15. Divide by. And I need to close the bracket twice. What is our discounted value will be equals to 16,875. Which is option four. And that's how you will calculate the discounted value. Any questions? No. I'm going to give you one question and then we move into compound interest. This is your question. How much simple interest is payable on a loan of 40,000 borrowed for 22 periods, 22 months period at a simple rate of 10% per annum? Pay attention to the question. How much simple interest? So it means they're asking you to calculate it. I will be very nice and give you the formula because I'm going to assume that at this moment you have not familiarized too much yourself with the formulas. So I'm just going to tell you which formula you can use. I is equals to P. R. T. That is the formula to use. So what is the fact given on this question? That is your exercise and then we can do feedback. I want to give you two minutes because this is easy to do. Are we happy? Are we done? Are we good? Yes, I'm done. Are we? Okay. So let's answer the question. What are the facts given? What is our P? P is 40,000. And what is our R? The interest rate of 0.10. And what is our T? 22 over 12. Good. Then let's substitute. That would be 40,000 since you have given me the values. It would make my life easier to just copy the values as I see them. 32 over 12. And for those who don't know how, let's show you how to answer the question. I'm not going to use my case, your calculator, fractions and all that. We're going to calculate this manual because it's a division and multiplication. They all have same priorities. So I can work from left to right or right to left. It doesn't really matter. So I'm going to first start with the 22 divided by 12. So 22 divided by 12. And I'm going to multiply the answer with 0.10. And I'm going to multiply the answer with 40,000. And the answer would be voila. Voila. 7, 30, 30, 30, 30, 30. Okay. So that's one way of answering the question. The other way, because they've got the same priority, you can just continue and say, I hope the calculator will disappoint, multiply by. I also want to bring to attention that your calculator has a percentage. So if I press there, 10, and I go shift and I go on the percentage side, because it's in orange, you can see that there it represented as a percentage. And then I go multiply that by 22 divided by 12. Because multiplication and division have the same priority and it will give me the same answer. It only works with multiplication and division. So it will still give you the same answer. Alternatively, I can use the fraction, which is 40,000. Now I'm just playing around with my calculator. I'm sorry for those who am wasting their time. So I'm going to use the same shift, 10%. And I'm going to put it in the bracket, then I'm going to open again my bracket, and I'm going to put my fraction and say 22 and move down and say 12. And close bracket and I press equal. And you will see that I still come back to the same answer. So you just need to know how to use your calculator. But I'm just playing around on my cashier calculator. Because this is the only last time that I'm using a cashier calculator to demonstrate probably. Okay, we're not going to answer this, but looking at this question, it says you can take a picture of it and then work it out. If you still unsure how to find the answer, we can discuss it on WhatsApp. I want to move to compound interest. We only left with 10 minutes or less. Dr. invested one half of his savings in a bond that is paying 9.5 simple interest per year for two years and received a 589 as your interest or as his interest. What is the value of his total savings making the investment? What they're asking you here is to calculate what would be his total savings. So now you need to think about it because yeah, they say they invested one half. You need to be able to take any amount and take one half of it and say that would be your investment where you will get an interest. Remember interest is they would have calculated it by using is equals to P. PRT, right? So you have your interest. You have your 9.5. You have your period for how long for two years. You can calculate your P, right? So if you know what your P was, you will know what your interest is. And then they just want to know what will be their total savings. So what is the one half? So subtract one half of to get the one half of that. That will give you your savings or the total savings. You will have to calculate based on that. That's one thing that you can calculate on your own. And I just want to see if you have learned something today that I haven't teach you or taught you that you can do on your own. In summary, in terms of simple interest, we've learned that interest is the amount you pay and we can calculate it by using that formula. I is equals to PRT, the future value of a simple interest. It's given by S is equals to P times one plus RT. And if we want to find present value, you can just change the subject of the formula and make P the subject of the formula by taking the accumulation factor divided by P. I will give you your present value for a simple discount. We also learned the same discount is the amount that is the amount that is discounted by that fraction. The proportion or the proportion and the discount value is the actual discount amount after you take out the discount on the discount, the discount from your present way. Okay, so now let's move to a new topic called a compound interest. If you have a financial calculator, you are able to use your financial functions on your calculator, but you need to practice. And you need to follow the steps I'm giving you because the steps are the same from today until you go write the exam. You will be using the same step is just changing in terms of what is given, but the steps are almost exactly the same. In terms of compound interest, you just need the calculator, whether it's a financial calculator or a physical calculator, you can still use your calculator, but more especially financial calculator saves time. And you need to also know the formulas because not always you need to rely on your calculator to do the calculations because they can just give you a formula and ask you if it's correct by just substituting the values into that formula. You just need to know how to substitute the values into your formulas and which formulas are correct and you need to know how to manipulate your equations. Okay, so in the next 30 minutes or 30 to 35 minutes, we're going to learn to do the basic calculation and not for time value of your money only for compound interest in this instance. So what is compound interest? It is interest on interest. So with the first one, which is simple interest, you only pay it once off at the beginning of the time. Simple interest, you pay it every type of depending on your periods if you take if depending on your compounding periods. If you are saying you want to pay interest on a monthly basis, you will be charged interest on a monthly basis and you will have to pay interest on that. And remember the interest you will be paying will be built you will be calculated based on the previous interests as well that you have and or you were included. So it's interest on top of other interest. When the interest is end on an investment and it's not withdrawn, but left in the bank, it will accumulate interest on top of it. So to calculate compound interest, the formula looks like this. The future value of compound interest is given by your present value or your principal amount times one plus the rate to the power of your period. Now, the other thing with the compound interest is the following because we talk about compound interest. We talk about the compounding periods. You need to remember and always know that on this formula, there are certain things that are not visible, but they need to be there. You need to know that your T is T, you need to multiply it with the compounding period. You need to know that this R you need to divide it by the compounding period. So what I will suggest you do is do this calculations outside of the formula and come back and substitute it into the formula with the actual T value that you would have multiplied with the compounding period. And your R value that you would have divided by the compounding periods and substitute them into this formula and you will see why because it becomes more complex. When you have your T value to the power of T times the compounding periods and so to clean it up, just do the calculations first and then substitute into the formula. So, and I've already said it today, R is divided by the compounding periods and T is multiplied by the compounding periods. Now, what is it that I'm talking about when I talk about the compounding periods? So your periods can differ, but always remember it has to build up to a year. Now, if we talk about a days like your periods are in days, then how many days make up a year? At 365, we do not include the leap years at this point. We only use the normal calendar without the leap years. How many weeks are there in a year? There are 52 weeks that builds up a year. How many months? There are 12 months that builds up a year. That is why when we were calculating quarterly monthly and all that, we were dividing the months by my 12th. If it was quarters, let's say they would have given you in three quarters, then we would have divided those quarters by four because we know that the quarters divided by four will make up a year. So if we talk about three months or quarterly, then you need to pay attention. In your exam or assignment, they might treat you by using words like in three months. It's payable in three monthlies or three months. You must know that three months make up a quarter and a quarter is equals to four, right? There are four quarters in a year. If they say six months, semester, by annually, half yearly, then you need to know that there are only two of them. A year is divided by two six months. The first six months and the second six months makes up a year. So there are only two of them. Even if you work with semesters, there is semester one and semester two, they make up two six months of the year. Okay, so there are two of them. A year, it can also be called one year or yearly or annual. Remember that if they say annually, they refer into a year. If they say by annually, they refer into half year or six months. So you just need to know the compounding periods. The right compounding periods to multiply with the period and the right compounding period to multiply or to divide the interest. So for example, if they say compounded monthly, know that 12% will be divided by 12. And your period, if they say it's two years, will be multiplied by 12. If they say by annually or half yearly, know that you will divide your interest by two and multiply your period by two. Okay, let's get that example. We're not going to draw too much on this. So calculate the compounded amount of 500 invested for 10 years at seven and a half per annum compounded annually. Now, what is it that the question is asking us to do? Calculate the compounded amount. Therefore, it means they want us to calculate the future rate. That is the future rate. What is it that they have given us? What are the facts given in this statement? We are given our present value. We are given the T. We are given the rate. So I'm just going to write, for now I'm just going to write the R of, we need to divide this. This is the same as 7.5. So it means it will be 0.075, right? And they told us that it is compounded annually. So our compounding periods are equal to one. That is very important to note and know. So it means, in a way, we would have multiplied our 10 years by one, multiplied our rate by one. It doesn't really matter. You can just leave it as it is because 10 times 1 is 10. But let's calculate. This is the formula that we need to be using. So we'll just substitute into this formula. We're looking for S. So P is 500 plus times 1 plus our rate will be 0.075 divided by 1. Did I multiply there? Multiply the state of divide. So we divide 0.075. This is just for explanation purpose. If it's compounded annually, you don't even have to worry about the one because 0.075 is the same as 0.075 if you divide it by one. 10 times 1, which will just be the same as 1 plus 0.075, which will give us 1.075 to the power of 10 and to solve the power. So we solve what is inside the bracket with the power. So 1.075 to the power of 10 gives us 2.06103. Multiply that with 500. And the answer we get is 1,080.52 because it's rent. Always remember money is always to 2 decimals. Your answer should always be in 2 decimals unless the options are in whole numbers. And then you just make sure that you round off correctly as well. Now this is when you are calculating manually, especially for those ones who do not have a financial calculator. If you have a financial calculator that looks like this, then the buttons here at the top are the ones that are important to you. You need those buttons plus the second function plus the on and off. What else you need? You need the ENT and your numerical value, but not only that, you also need this plus or minus. It's very important. So those are the most important buttons you're going to be using. So let's answer the same question using our financial calculator. Now, this is very, very important, especially now while you are still busy with your assignment and in preparation for you to go and write the exam, you need to practice. This you cannot remember overnight before the day you go write the exam. The steps I tell you, they are almost exactly the same from now on until we get to amortization, but you need to practice. And practicing means you don't have to just jump and go onto your calculator and start calculating. Write the steps down before you use your calculator so that you make sure that you have my bag. I'm load shedding. Are you able to hear me? Hey, are you? Yes. I am load shedding. I needed to connect quickly to another. So it's very important to, I'm not sure where you lost me actually, but anyway, you need to make sure that you write the steps down. So the first step on using your calculator, it's always clearing your calculator. By pressing, I forgot to also include the mode button. So you go into press second function. You go into press second function and then press the mode button where they see a on top. That is the first step on every time you start doing any calculation. That is very important because everything we're going to be doing right now. You're going to be storing the information in your calculator. If you don't clear your calculator, you will still have data stored or the numbers stored in your calculator and you might get the wrong answer. So make sure that this is the first thing you do. Second function CA. Then we need to capture the compounding periods. So to capture the compounding periods, we're going to press first second function. And you go into press on top of I and Y. There is the orange button that is P slash Y. That is our compounding period function. And for now, because it's for practice papers, we're going to do this step. And you're going to press button number one, which is one for the compounding periods because they were yearly. So it's one and you're going to press E and T. And once you have done that step, then you are ready to go to the next step. You need to press on and off your calculator. Once you have captured your compounding periods, you can go on and off your calculator. And now you are ready to capture this information given what information I'm talking about. We know that we're looking for S or right now I need to change the technique. So the compounded amount now changes on your calculator. You're going to write FV because that's what we're going to be using on your calculator. This changes to PV because that's what we have on our calculator. The number of years that is N, we're going to capture it on N. And our rate is going to change to I and Y. Now, the other thing that I need to stress is that remember in the manual thing we said the period we multiply with the compounding periods, you're still going to do that. Nothing changes when it comes to the period. The interest we said we divide by the compounding periods. Now I'm going to tell you that for the interest when you are using a financial calculator, you're going to capture it the way you see it right now. You're not going to divide that by a hundred. You capture it the way you see it. You are also not going to multiply it with the compounding periods. The calculator will do that automatically in the background, in memory. Okay, so that explaining that. Now let's capture the information given. The first one that you need to capture is very, very important for a present value, future value payment. Every time you capture those three things, one of them should have if they are all in the question and you are given all of them and you need to capture them. Only one of them will have a plus or minus in front of it. Otherwise, if you don't put a plus or minus on any one of them, your answer will be negative. So the first thing you do is press plus or minus and then press the value, which is 500 and then press present value. Very important, plus or minus, not the plus or minus. Some people like to press the subtraction and addition, not that one. This function right here, the plus or minus of the function that is part of your calculator. The plus or minus and then you press in the value of your present value because that's the value they gave you. If they're giving us the future value, we would have put plus or minus the future value. So the value of the future value. So once you have captured your present value, now let's put in my computer stack. Now we put in the interest. With interest, remember, this is 7.5. So with interest, always remember you capture it the way you see it. So you go into just press 7.5. You're just going to press 7.5 and my laptop battery is almost done. 7.5 and you press the I and Y button. You just press I and Y button, it will store your interest. The next one is to put in the period. Putting in the period, we first press the period. So it's 10 and then you press second function. And because we press the second function, it means we calling the orange button there, this orange button. And then we need to store the value and then you press N again. You will press N twice. So you will say 10 second function and N again. So this step is the same as pressing N and N again, because second function N and then press N to store the value. And you will see that it will say 10. You will, you would have pressed 10 and then multiply by the compounding periods and when you press N, it will give you the actual value. If it was N times 12, it will give you 120 after you press the second value. Okay, so now we are ready to compute or calculate our future value. The only thing you do is press COM, which is this compute future value. Those are the only two things and when you press that, it will give you 1030.52. You have followed the same step on your calculator in order for you to be able to see what I have just done. Unfortunately, I do not have an emulator for a sharp financial calculator, so I can't show you on the screen. I only have a manual one and now with my network done, the house is dark city and I can't even open any other application on my computer and the battery is almost finished. I hope it won't allow us to finish the session. How long do we have? 15 minutes. How long do I have? Battery life. Let's all see. I have 49 minutes, which it will get us to the end. I should minimize the brightness. Unfortunately, I cannot close any application on my computer, but it's fine. 15 minutes, we will get through it. Okay, so now let's recap on what we just learned. So we've learned how to calculate the compound interest. Now, what we haven't done, it's a lot of exercises. We're going to do that just now, don't worry. In the next 15 minutes, we'll look at more exercises. I just want to bring two attention, especially those with no financial calculator. You need to be able to know how to change the subject of the formula. For example, if they ask you to calculate the period, how long and they gave you and they said it is time compounded quarterly or yearly, then you need to know how to get T down by using the logarithm. You need to know how to use the log. In BNU, where they do not teach you, the logarithm also is. In BNU, they do not teach you the logarithm, but in QMI, they teach them the logarithm. So you'll only learn about the logarithm in QMI than in BNU, but you are expected to know how to answer questions like this. So you need to go and practice and learn how to change the subject of the formula, or you will need to go and memorize or write down or keep it safe somewhere, all this iteration formula so that you can use them to answer your question. For example, like if they ask you to find R, it is inside a closed bracket and it is to the power of a value. So how do you get that? You need to be able to know how. So this is part of exponents and powers. We didn't cover that section, but you just need to know how to manipulate the expressions as well. Now let's get more exercises. Let me not stress you even further. So those with a financial calculator, you do not have to worry too much about this, but you need to also know how to do this. In case they ask you a question relating to this, they just substituted the values and they ask you which one is the correct way of substituting and calculating R, the rate or the how long. So you need to know also, but you don't have to know how to calculate it using that because your financial calculator steps are as easy as ABC. So let's look at this question. I'm going to do one and then you guys do one before the end of the session. So calculate the accumulated amount after three years if 5000 is invested at an interest rate of 10% compounded quarterly. So what does the question ask? Calculate the accumulated amount, which means I am going to do this one for the manual people first and then we're going to do for the financial calculator. So you will go ahead and say accumulated amount, it means they're asking me to calculate the future value. After three years, that is how long, that is T, if 5000 is invested, therefore it means this will be my present value and an interest rate of 10% that is my rate and it is compounded quarterly. Therefore my compounding periods, they are four. Now immediately after doing that, you go back and you say three times four is equals to 12. The P will stay and you go to the rate and say 0.10 divide by four. Remember we divide by the compounding period and you can even go ahead and find the answer. Now if it's long, then I will suggest that you just use it as it is. So let's see, 0.10 divide by four is 0.025. That is my rate. So we need to calculate S is equals to T times one plus R to the power of T. I'll just substitute the values that have already calculated. So it's 5000 times one plus instead of using 0.10 divide by four, I'll just use 0.025, which makes it easier. To the power of 12 instead of using three times 12, I just use the value as I see it. So this will be 5000 times 1.025 to the power of 12 and I can get the answer. So the answer would be, I'll need to take out my calculator and do the calculation. Okay, because my thing failed, that's why it does this. I don't have a calculator right now. It's 6,724 and 44 cents. 6,724 and 44 cents. Yes, number two. Thank you very much. That is, if you have calculated manually, if you have a financial calculator, this is what you will do. So with a financial calculator, you will go ahead and do the same. Identify what the question is asking you to calculate. So you will say that is the future value, right? The amount, how long? That is the period, which is your N. The present value that PV, your interest is I slash Y. The quarterly compounded periods, you can write it as P slash Y. Because you're going to remember which one is which that you're going to be using. So the first step you do, second function, C A. You see, what I'm doing is what I expect you to do when you answer questions like this, especially now when you are practicing, right? Then second function, P slash Y, and then you put in the compounding periods. Then we fall and you press ENT and you go on and off your calculator. Then we are given the present value. So plus or minus 5,000. And that is our present value. You will press the present value function. And we can press three, let's start with the interest. Interest is 10. So you will press 10 and press I and Y. Remember, as you see it, 10 is 10. You don't divide it by 100. You just put it as it is. And the period is three years. You put the three, you press second function. And here, because I don't want to write multiply by N and I'm just going to say second function and then press N and twice, because you need to press N twice, right? And when you are done, you say, come FV and the answer should be the same as 6,724 and 24 cent. You will have to practice doing the steps in order for you to be able to know how you will see when we do annuities. We just change present values and future values to payment and future values and payment and present values. They just the same. We only change that part and this part. That is the only thing. If you are asked to calculate interest, you will be given future value. So if you are, if you are calculating the same and they gave you, they want you to compute interest, comp, I and Y. Then you will just do plus or minus your PV and you will put the value of your future value without putting the plus or minus. Remember, only one of them will have a plus or minus and then you will do your value. Remember that will be your value, the value second function and, and again, and then comp, I and Y. You just swap around. I like those who are calculating manually. If they didn't give you R or they're asking you to calculate R, you will have to manipulate this equation to get to R. So for you, you just write the steps as they are. You can see that the steps, the only thing that doesn't change is the top part. They will always stay like that for every step. You first start with clearing your calculator and then capturing your compounding periods and turning your calculator on and off. And then you can do all the manipulation here at the bottom. The top part stays for all the calculations. They will be the same. The only thing that changes is what you are given, the facts given and what you need to be calculating. Okay, enough with me saying a lot of things. So let's look at more activities. So this one is your example. I'm going to give you the formula. I'm going to give you the steps for those who are doing financial calculations or using a financial calculator. I expect both of you to work it out and then we can compare the answers. So with a deposit of 1200, Deborah opened a savings account paying 5.8 interest annually. Compounded monthly. She agentally withdrew a sum of 800 after five years. How much will she have acquired in her travel account four years after withdrawing the 800? The amount must be rounded off to the nearest. So here is the catch with all this. You will have to calculate how much they have saved up in five years time. And then you will have to take the balance of that five years time and calculate four years to see how much she would have had after withdrawing the 800. Because four years after withdrawing the amount is you are the interest will be ending on onto the balance that is still there in the account, right? So let's first calculate the five years. So you will use S is equals to your P times one plus your R to the power of two. Those ones calculating with a calculate a financial calculator, second function. The A unless if it's me. Oh yeah. And second function. P slash Y. Where I put blocks, it means you need to replace it with the actual value. And then you will press E and T. And go on and off your calculator. Plus or minus. And this is the deposit, which is the present value. And our interest. Which is I am why. And you need to put the amount how long five years. Which that is. Second function. And, and again. And then you will need to come. What do you need to come up here? You will need to come. Future value. And then once you get the answer of a future value, you will need to subtract. What I forgot to do here is also for you. Once you have calculated this, you will need to subtract 800. And that will give you your balance after five years. But remember it says. How much. She would have a cute in her travel account for years. After withdrawing the internet. So it means from getting that S we need to calculate another S with the new balance. With the new new money that is on the. That it will be left to the power. So also the same. Once you get this, you go back. You go back there. You change only that value you say plus or minus you get the value. So you will get the answer. The answer you get, you just, you don't have to change everything. You just say you repeat the step. Plus or minus. And you put there the present value. You don't have to change the interest. You just change the period. It's four years. And yeah, instead of five now, you just say four second times in that. So the only steps for the second time you change are those two. And then you come. Future value. And the answer you get that should be the answer. And no, it's not just the answer because. Yeah, that will be the answer because they want to know how much they would have. Acquired. And remember those who are calculating manually. You are. You need to divide zero comma zero five eight by the compounding periods. There are months. So you divide by 12. Your periods also remember. It will be five multiplied by. 12. Don't forget that. Are we winning? And remember they say rounded off, right? If not, let me help you because we are, we are out of time. So you just go ahead and I'm just going to remove this step that I've added right now. Yes. So that then we can have the answer properly done. 1200 times one plus our rate. I don't have the answer to that. 0.0. Five eight divide by 12. To the power of. Five multiplied by 12. And. When you do this, probably the answer will be 1600. The answer is 1600 point. Five nine. And we need to subtract 800 remember I had the 800 there. If we subtract 800 because they say she withdrew that much. She takes away the 800 then she will be left with. 802. Point 59. Right. And. We need to take this. How much accurate after four. Yes. We take our new eight. Oh two point five nine. Multiply by one plus our rate because they didn't say anything whether it changed or not. So we're going to assume that is still. The same. Right. And because now we know that it is only after four years, so it will be four times 12, which. You can calculate and that gives us. One. The answer will be. One thousand one one point. Six zero, but they said. You need to run it off to the nearest rent and therefore to the nearest rent. This is one. One. One two. That is the nearest rent. In terms of the. Financial calculation. Compounding periods there are monthly, so you will have on your steps, you can just double check if you can check everything correctly. You just press the 12. And you press. One thousand two hundred. You would have pressed five point eight. And you would have put in five years and compute. The answer and then you will still also get the same as what they had, which is one thousand six hundred. And two point. Five nine and then you subtract eight hundred. And the answer you get would have been eight or two point five nine. So what you do, you don't have to pay your calculator in this instance because it's still the same thing. You just press plus or minus. And then you press the eight oh two point five nine. And then you store the new number. That's what you do. I asked a lot of them off guys. That battery died. And it leaves. It leaves your batteries or it does. No, it's a mule. Especially if you don't have that financial calculator money. Yeah, it's a young thing. I'm not out of the track. I'm not out of the track. You must stop the recording people. Oh. Okay, let's go and make eyes. See you later. Okay. Bye.