Future Value Grade 12 | Introduction #Finance

welcome to grade 12 financial maths please note that in this CashNews.co course i am not going to be going over previous year financial maths but i do have courses available on the website so just go to the all courses tab and you can look for grade 11 financial maths grade 10 financial

maths it’s all there this in this grade 12 course i’m just going to be focusing on the new concept for grade 12 and that is an annuity now i’ve seen students who get they pretty much go through the whole of grade 12 and still don’t grasp the idea of what they are trying to

teach in grade 12. in grade 12 we are introduced to something called an annuity now what an annuity is is the following well let me first explain about what you did in grade 11. so in grade 11 you would typically have a question like this you would have a person who exam for example invests 500

rand into an account and then maybe add 400 grand in three years time or they take out 200 grand and then the interest rate changes an annuity however that is not what an annuity is an annuity is something like you would like to save up ten thousand rand in five years time for example and you would

like to do that by making regular payments of the same value at specific intervals so for example you might want to make monthly payments so you will make the same you pay the same amount every single month or you’ll pay the same amount every year or every quarter or every six months for

example so you do something regularly so here’s the difference in grade 11 you would be asked a question such as john invests 500 rand in a Savings account which earns 13 per year compounded monthly calculate how much john will have in five years so for that type of question

you would simply use the compound interest formula where your starting amount would be 500 rand your interest would be 13 which is 0.13 you had compounded monthly and for 5 years you would say 5 times 12. in grade 12 it’s slightly different john invests 500 grand each month into a

Savings account which earns 13 percent compounded monthly calculate how much john will have in five years you see the difference is is that now john will be paying 500 grand every single month he’s not going to just make a once off payment and let it grow he’s going to

make multiple payments so what you could imagine is that you would for for example the first 500 round that he pays well that would be in the account for five times 12 then you would have to add that to the next 500 grand which would earn a little bit what could earn less interest because the first

payment that he makes will be in the bank account for the longest the second payment that he makes will be in the account for 59 months because 5 times 12 is 60 so this one would be 59 then you would have to add the next one which would be in the account for 58 months and you would have to add all

the way to the very end when he makes his last payment of 500 rand and so what i’m going to do is give you a brief a brief a brief overview of how they came up with the formula that we’ll use because otherwise it’s going to take a long time you’d have to do like 61 or 60

different calculations because this number would have to go all the way down to there so first thing we need to look at is we’re gonna pretend well we’re gonna we’re gonna do our calculation starting at the very end and going in that direction it just makes the maths a lot easier

so let’s see what type of sequence we form if we go in that direction we’ll have a look what’s happening the first term is 500 then it’s 500 1 plus 0.13 over 12 to the power of 1. then it’s the same thing to the power of 2 and then it’s the same thing it would be

to the power of 3 and then it would be to the power of 4. can you see that that is actually a geometric sequence where the common ratio is this because if i take the number 500 and then i times it by that then i’m going to end up with 500 one plus 0.13 over 12. and if i times that by another

one of these then i end up with 500 1 plus 0.13 over 12 to the power of 2. so we’ve got a geometric pattern on our hands and i want to quickly mention this 500 rand is the last 500 round that john would spend right at the end of his account this amount here was made one month before the

account closed and that’s why it gets one month’s worth of interest this was the payment just before so it gets two months worth of interest and bloody bloody blah so remember the uh geometric sum formula which went like this but i’m just going to switch it around so that

it’s rn minus 1 and r minus 1. remember in that geometric CashNews.co in series and sequences i did say that you can do it both ways you can either have it as 1 minus n over one minus r or you could have it as r n minus one over r minus one i’m going to choose this version and to make

the maths very easy we’re gonna start at the beginning with at the at the end of john’s account so that will be this 500 we’re not going to start at the beginning over here we could but it just makes the maths very complex so a is going to be term 1 which is 500 r is going to be

the common ratio which we said was 1 plus 0.13 over 12 to the power of n minus 1 and that’s all over r which is 1 plus 0.13 over 12 minus 1. now at the bottom the ones cancel and so we just end up with 0.13 over 12. and so here we have something called a future value formula and so the future

value formula goes like this where the future value of your account is equal to your monthly payment which in this case was 500 see there it is 1 plus i so there’s the 1 plus over here to the power of n to the power of n minus 1 we have the minus 1 over and then i think we’ve just lost

this part over here i because remember we said that these ones cancel and so there we have i so this is a formula that adds up all of those payments so remember john makes monthly payments and each of those little payments is going to earn interest some of them will be in the in the bank account

for long some of them will be in the bank account for a very short time however we want to add all of them together so we use the sum formula for a geometric sequence which takes on the following form and we just call it f v to represent the future value of the investment there is a different

formula called the present value formula but that will discuss in later CashNews.cos