Maths compound interest problem

Question

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A man borrows Rs 10000 at 10% C.I. compounded yearly. At the end of each year he pays back 30% of the sum borrowed. How much money is left unpaid just after 2nd year?

Answer 1

This problem can be done by "brute force" pretty efficiently. If the annual interest rate is 10%, then you can calculate the balance at the end of each interest period (before the payment is made) by multiplying by (1 + 0.1) or 1.1.

At the end of year 1, the 10,000 becomes 10,000(1.1), or 11,000. Then 30% of the amount borrowed is paid or 10,000(0.3) = 3000. This leaves an unpaid balance of 11,000 - 3,000 = 8000.

At the end of year 2, the 8,000 becomes 8,000(1.1) = 8,800. Then another 3,000 is paid, leaving 8,800 - 3,000 = 5,800. So the unpaid balance is 5,800 at the end of year 2.