Comparing yearly and monthly compounding
Comparing yearly and monthly compounding
IP 2
8 marks
Plan \(A\) pays \(3.5\%\) per annum compounded yearly. Plan \(B\) pays \(3.4\%\) per annum compounded monthly. Assume no deposits or withdrawals after the initial amount and that the rates do not change.
- Find the amount in each plan after \(5\) years when \(\$10\,000\) is invested, and state which plan is better.[3]
- Find the percentage by which a balance in plan \(B\) grows in one year. Explain why it is greater than \(3.4\%\) but plan \(B\) is still worse than plan \(A\).[2]
- Find the least whole number of years for an investment in plan \(A\) to at least double.[3]
Solution:
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Answer:(a) \(A\): \(\$11\,876.86\), \(B\): \(\$11\,850.20\); plan \(A\) (b) About \(3.45\%\); interest on interest raises it above \(3.4\%\) but not to \(3.5\%\) (c) \(21\) years
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