Financial Maths grade 12 Exam Questions #Finance

Michaela buys Furniture to the value of 10,000 Rand she borrows the money on 1 February from a financial institution that charges that interest rate compounded monthly Michaela agrees to pay monthly installments of 450 the Loan allows Michaela to start paying equal monthly

storment from 1 August okay calculate the total amount owing to the financial institution on 1 July okay so let’s break this down um on 1 February Michaela borrows money borrows money now normally if you’ve watched all the CashNews.cos on present value and even on the future value when

do we normally make our first payments normally it’s after 1 month so usually we would make our first payment over here okay then it would be 1 April you would make your next payment so this would be your normal or normally your first payment this would normally be your second payment third

payment whoops June sorry 1 July and 1 August okay now Michaela only starts making her face first payment over here so how many payments did she miss well you mustn’t count this one because normally we start over year so she misses 1 2 3 4 5 she misses the first five payments now remember if

you’ve watched CashNews.cos on present value the value of the Loan that she took out is 10,000 Rand that institution like the bank for every every payment that you’re missing remember that that Loan amount is going to keep growing okay so that 10,000

Rand is no longer going to be 10,000 Rand when she decides to make her first payment she’s going to log into her appsa or her FNB account see that the Loan amount is no longer 10,000 Rand maybe it’s now going to be 10,600 for example because she hasn’t started

paying but the bank’s not going to wait for you they’re going to start adding on that interest okay so the first question says calculate the total amount that she owes to the financial institution so obviously it’s not1 ,000 Rand anymore so we’re just going to use the grade

11 formula and we’re going to compound that 10,000 Rand for 99.5% I like to write it like that compounded monthly and how many payments did she miss five okay and so let’s see 10,000 42 round 15 so you mustn’t say y but Kevin we’re starting here on 1 February and then

it’s going to be 1 2 3 4 5 6 months until 1 August it doesn’t work like that guys you got to think about how it normally how they normally do it in the real world so in the real world you normally start after 1 month so they don’t penalize you for not starting there and then

they’re only looking at the payments that you miss okay so because she’s starting here they’re not going to also count that part there so the missed payments is five and so this is how much the new Loan amount is um when Michaela decides to start paying this next

question says how many months will it take Michaela to pay back the Loan okay so we now know that we’re not going to start over here now we’re now going to look at from when she starts paying okay so we’re going to use the present value formula which is p = to x 1

– 1 + i n / I so now we no longer using 10,000 we’re now using 10,425 the monthly payment is 450 the interest rate is 99.5% so 0.095 okay I’m not going to fit that in and now okay so the number of payments we don’t know so we can actually just leave that as the unknown and

then we could just say 0.095 over 12 you see so it’s actually an easy question um just don’t use 10,000 because that’s no longer valid you got to make it valid from where we starting and now we’re starting to make our payments here so this is the amount you would use and

they’re not saying like in what year would she finish or whatever they just want to know how many months and so you can literally just go work out the value of n now and yeah so let’s do that so what I would do is I would multiply this part over to the left and I would divide this part

on the left as well as well and so that would end up giving us 10 40215 multip 0.095 over 12 IDE 450 and that’s then equal to 1us now this I will typ on my calculator the 1 + 0.095 / 12 but leave it as a fraction okay it’s very sensitive cuz we’re probably going to use logs just

now and your answers can change a lot if you start rounding off now so leave it like that okay type this in your calculator as well it’ll also give you a fraction let’s see what that will be oh it doesn’t give us a fraction okay that’s fine going to double check 0.095 over2

450 okay then just write all the decimals don’t want to be rounding off at this stage okay now um I’m going to take this unit to the left and then bring this to the right and so now we end up getting um 2 419 9 over 2,400 to the N we just brought this over to the left hand side and then

on the right hand side you’re going to get that now I’m just going to quickly pop that on my calculator and so we end up with 2419 over 2,400 to the N equals to 0.816 9 213 okay now logs so with logs you take your exponent you make it equal to log of your base your base always stays

your base whether you’re going from exponential to log or log to exponential your base stays your base so this was the base and now it’s still in the base position so that’s a nice thing to remember and then 0.816 999 213 okay so it would look like whoops what did I just do like

that okay so let’s go type that in okay so that’s going to give us n = to – 25.6 3 and so n would be 25. 63 so what does that mean is it going to be 25.6 3 months well no you can’t make 25.6 3 payments so she’s going to have to make 26 payments where the last payment

will probably will definitely will be a little bit less than then the normal I’m surprised they didn’t add 7.2.4 asking us to calculate what that F final payment amount would be we’re lucky this next question says what is the balance of the Loan immediately after

Michaela has made the 25th payment this last one says what is the balance of the Loan that actually just means outstanding balance so I’ll start with the Present Value method you only need to do one in the exam though okay and then I’ll show you the future value so with

present value this n value is payments you st need to make okay so remember when we calculated N I said 25. 63 but when you use this method you actually have to use the non-rounded method the non-rounded value so 6315 128 so it says after we have made the 25th payment so what you then do is you

just say minus 25 and that will give you the number of payments or the part of the payment that still needs to take place I know we can’t make that many payments but that’s the portion still left and that is what we use here for this formula and so you’re going to say 450 1 minus

1 plus uh the interest rate was 9.5% and we are going to say 0.631 5128 and that is all going to be be over 0.095 over 12 if we calculate that we get 282 Rand and 36 Cents now when you do future value your outstanding balance is you got to do two parts it’s the Loan amount

minus your future value of your payments so your Loan amount is just using the grade 11 formula a = to P1 + I the n so that’s just going to be um your original Loan amount which was not the 10,000 you got to use the 10,000 it’s from when we started

paying we know that we’ve done 25 payments from that moment and then um 1 + 0.09 okay I’m definitely going to run out of space okay I’m going to erase the present value cuz you get the idea so it’s here future value okay so we said that your outstanding balance is always

going to be your Loan amount whatever that’s become minus your uh future value so that’s going to be you’re using the grade 11 um a = to P1 + I to the N formula and then this is going to be your future value now with this formula we you the N is the number of

payments that are already completed it’s not the number of payments you still need to complete it’s the the number of payments that have already been completed whereas when we used the present value then it was different okay so it’s going to be uh the original or the the the

Loan amount when we started paying we’ve made 25 payments at this part our our monthly payment is 450 and that’s 25 payments okay and that’s it so now you can just go type that on the calculator that gives us 282 36 sometimes it doesn’t give the exact same

answer as the Present Value method sometimes it’s a little a few cents off and there we go now some of you might be thinking Kevin why aren’t we why aren’t we now taking this answer and compounding with one more month Ah that’s a good question that’s only if they asked

us to calculate let’s say they added a new question 7.2.4 calculate the value of the final payment then you would have to realize that this number here is your outstanding balance after to 25 payments your 26th payment is going to happen in 1 month and that is where we would then compound

using the grade 11 formula for one month maybe you’ve seen CashNews.cos of mine of that before but this question isn’t asking that they just want to know what is the outstanding balance immediately after that 25th payment