Question

A sum of $10 000 is placed in a bank account and earns 12% interest per annum, compunded annually.

How much money is in the account at the end of 6 years, just after the final interest has been paid?

Answer 1

10,000 is the initial money, and then next year I have 112% of it, right?

Answer 2

And every year, I have 112% of the previous year's amount, right?

Answer 3

This is what I did.
Let A_n be the amount at the end of nth year.
\[A_1 = 10 000\left(1+\frac{12}{100}\right) ^{1} = 10 000(1.12)\]
\[A_2 = 10 000(1.12)+10 000)(1.12) => 10 000(1.12)^2+ 10 000(1.12) \]
.
.
\[A_6 = 10 000(1.12)^6+10 000(1.12)^5+....+10 000(1.12)\]
\[= 10 000(1.12)+.....+10 000(1.12)^5+10 000(1.12)^6 \]
then its a G.P
\[\frac{10000(1.12)(1.12^{6}1)}{1.12-1} \]
but apparently the answer is wrong..

i havent done these in a long time im not sure..

Answer 4

So, at the end of 'n', years, I have my original amount made 112% 'n' times, over and over again.
So, I have at the end of 'n' years, amount 'A', which is
\(A = 10000(1.12)^n\)

Oh no, you just need the nth term not the sum!

Answer 5

The bank, unfortunately, till now has no such investment-programs, where we receive the sum of our account balances at the end of each year.

Answer 6

it says at the end of 6 years; then the whole thing right? lol

Answer 7

nevermind i figured it out

Answer 8

good then..