2021 DHS P1 Q10

Mr Safe takes up a bank loan of \(\$M\) for an investment plan. The loan amount compounds at an annual interest rate of \(100r\%\), where \(0 < r < 1\).

1. By considering the loan amount at the end of \(6\) years, find the range of values of \(r\) such that the amount of compounded interest will not exceed \(20\%\) of the initial loan.[3]

Take \(M=20\,000\) for the rest of the question.

Mr Safe invests \(\$10\,000\) and \(\$10\,000\) in Scheme A and Scheme B respectively for \(6\) years, with the two schemes starting at the same time.

Scheme A:

To receive payouts at the end of every month, starting from \(\$10\) and increasing by \(\$0.30\) every month.

Scheme B:

To receive payouts at the end of every month, starting from \(\$10\) and increasing by \(2\%\) every month.

At the end of \(6\) years, the principal sum of \(\$20\,000\) is returned to Mr Safe.

2. Find the total monthly payouts Mr Safe receives after \(n\) months, leaving your answer in exact form.[4]
3. Find the set of values of \(n\) such that the total monthly payouts from Scheme B exceeds that of Scheme A.[2]
4. Given that the annual interest rate of the bank is \(2\%\), determine whether it is worthwhile for Mr Safe to take up the bank loan for the investment.[3]