Financial maths grade 11 | Loan #Finance

hello everyone so welcome to this lesson in this lesson we are going to look at a Loan so a Loan is an amount of money that you typically get from the bank and then you will have to pay that Loan back over time and they’ll obviously

add interest onto that so in some of the previous questions we we always wanted to know how much money we have at the end of a certain period so on our timeline for example we would add money at various places so like for example here you would add 3 000 Rand here you would add 2 000 Rand and at

the very beginning you would maybe add a thousand Rand then what you would do is you would take each of those amounts and you would drag them forward to the end date okay because we always wanted to know how much you have in the future however with most Loan questions not all of

them you typically want to know how much the Loan was in the beginning so you want to take each of these amounts that we’re going to use in the question and you’re going to drag each of them backwards so instead of going forwards you’re going to go backwards

I’ll show you how that works now because they’re asking us for the original value of the Loan now how would you know what the original value of the Loan is by looking at what the Loan is worth in the future or knowing what the

Loan is worth at the beginning well that’s at the beginning for example let’s say you take out a Loan of a hundred thousand Rand well that Loan is eventually going to grow to maybe 150 000 Rand because they’re going to add

interest so you’re going to borrow a hundred thousand from the bank and you would pay back 150 000 but if someone asks you what was the original Loan amount it’s not this amount it’s this amount over here so we are interested in the starting value so let’s

draw a timeline just showing all the different payments okay so it’s going to be like this t0 we don’t know how much the Loan is worth so that’s what we’re trying to figure out they tell us that the first payment will be made after the first year so at T1

he’s gonna pay back 5 000 Rand because they’ve told us that it’s three equal payments of five thousand Rand then after the second year he makes another payment of 5 000 Rand and then after three years he well that’s at the end he makes his last payment of five thousand Rand

they tell us that interest is going to be for the entire duration it’s going to be 15 quarterly okay so I’m just going to write that like that so all we do is you look at each amount so you’re going to look at this one first and you’re going to try work out what that one was

worth in the beginning so you know how we use the formula a equals to P1 plus I to the power of n you want to know how much that 5000 Rand was worth in the beginning and it’s going to be less so you could think of it as a is equal to 5000 Rand but you want to know what the starting amount is

okay so you don’t know what p is then you could go one plus 0.15 over 4 because it’s quarterly and then if you’re going from T1 back to t0 that’s only one year so that’s going to be to the power of 4 over here now if you wanted to get P by itself you would end up doing

this 5000 over 1 plus 0.15 over 4 to the power of four now what most teachers do is they bring this bracket over here they take it to the top now we know in maths that if you have something like 1 over X and you want to take that x to the top it becomes x to the minus one or if we have one over X2

then it becomes x to the minus 2 if you take it to the top so what we can do is get P by itself by saying 5000 and then saying 1 plus 0.15 over 4 to the negative four and what that question well what that will do is it will work out the original value of this 5000 Rand on day Zero so you’re

dragging everything backwards so you don’t have to go do the whole a equals P 1 plus I to the power of n and then get P by itself all you can actually do is you’re going to take each amount okay so we know that the 5000 that first five thousand it’s going to end up having a

bracket next to it of 0.15 over 4 to the minus four then you’re going to plus that with this five thousand Rand which is going to be 1 plus 0.15 over 4 2 and that’s two years now so that’s going to be to the negative eight and then the last five thousand Rand which is this one

over here that needs to go all the way back so that’s three years so you see how it’s the same as the previous type of questions but we just use this negative over here these negatives are a mathematical way to take the money to the left hand side and not to the right hand side and so

then you can just go type all of that on the calculator and that’s going to give you an original Loan amount of 11 254 Rand and 34 cents so in summary if you want to know the value of something in the future then you drag the amount forward so for example this five thousand

Rand if you drag that forward then that would be two years and so that would be to the power of 8 but it would be a positive eight if you want to know the value of something at the beginning which is typically used with Loans then you’ll drag it backwards so how many years do

we have in between those two well that’s only one year so that would be to the power of minus four if we are compounding quarterly but you must use the negative as that is the mathematical way to make the money go that way