Find the amount on Rs 8400 for 16 months at 15% per annum, the interest being compounded every eight months.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Rs 10164
When interest is compounded every eight months, the rate for one period is the yearly rate times \(\displaystyle \frac{8}{12}\), and the number of periods is the time in months divided by 8.
Rate per period \(\displaystyle =15\%\times\frac{8}{12}=10\%\)
Number of periods \(\displaystyle =\frac{16}{8}=2\)
Amount \(=8400\times1.1^{2}=8400\times1.21=10164\)
The amount is Rs 10164.
Why the other options are incorrect
Option (2) Rs 11180.4 — Incorrect. This uses 3 periods instead of 2; 16 months hold only \(16\div8=2\) periods.
Option (3) Rs 1764 — Incorrect. This is only the compound interest, not the amount.
Option (4) Rs 10080 — Incorrect. This is simple interest: \(8400\times\frac{15}{100}\times\frac{16}{12}=1680\), and \(8400+1680=10080\).