A borrower is repaying a loan with payments of $3000 at the end of every year over an unknown period of time. If the amount of interest in the third instalment is $2000, find the amount of principal in the sixth instalment. Assume that interest is 10% convertible quarterly

Answer 1

Messy question.

Since the payments is made annually, but the rate of interest is compounded quarterly, our normal formulas won't work. We have to convert the interest rate to match the payment period
let the annual rate be i
1+i = (1 + .025)^4
i = .1038129

let the original loan be $x
balance after 2 years = x(1.1038129)^2 - 3000(1.1038129^2^2 - 1)/.103829
= x(1.1038129)^2 - 6311.4387

interest on that is $2000

[x(1.1038129)^2 - 6311.4387](.1038129) = 2000
x(1.1038129)^2 - 6311.4387 = 19265.4303..
x(1.1038129)^2 = 25576.8690...
x = $20,992.1275...

Now that we know x, use the same steps as above to find the balance after 5 years.
then multiply that by .1038129 to get the interest, subtract that from $3000 and you got the principal. Before you proceed, check my calculations. I have a calculator with several memories, so I stored each intermediate answers and did not round off anything yet.

Another good part of the question would be to find the length of the loan.