Question

A person borrows $100 000 at the beginning of a year and agrees to repay the loan in
ten equal instalments at the end of each year. Interest is charged at a rate of 6% compounded
annually.
(a) Find the annual repayment.
(b) Work out the total amount of interest paid and compare this with the total interest
paid when repaying the loan in five equal annual instalments instead of ten.

Answer 1

We want to use the compounding interest formula that I will attach here:

Answer 2

Okay but also need to use geometric series too.

Answer 3

This an online calculator that can get you your answer for part (a) https://www.mlcalc.com/loan-calculator/100000-10-6-2021-1.htm

I don't quite remember how to approach it mathematically but @jhonyy9 or @AZ might be able to help when they come online

Answer 4

Part B I can help with because we are just plugging in values into the formula I attached before
\(A = P(1 + r)^t\)
In this case
P = 100000
r = 0.06 (the decimal representation of 6%)
and
t = 10 years

Answer 5

\(A = 100000(1+0.06)^{10}\)
^solving for this will get us the total amount we will have paid after the 10 years

we would then subtract 100000 to get the amount of interest we paid

Answer 6

I wasn't sure if there was some special formula for calculating the annual payment either but it just seems to be

For annual payments:
total amount (including interest) / number of years

For monthly payments, you'd just divide the total amount by the total number of months which is what that calculator you sent earlier did