A sum of Rs \(x\) amounts to Rs 15680 in 16 months at 18% per annum when the interest is compounded every eight months. What is the value of \(x\)?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Rs 12500
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 \(\displaystyle =18\%\times\frac{8}{12}=12\%\)
Number of periods \(\displaystyle =\frac{16}{8}=2\)
\(x\times1.12^{2}=15680\), that is, \(1.2544 x=15680\), so \(x=12500\)
The value of \(x\) is Rs 12500.
Why the other options are incorrect
Option (1) Rs 13000 — Incorrect. Rs 13000 grows to \(13000\times1.12^{2}=16307.2\), not Rs 15680.
Option (2) Rs 14000 — Incorrect. Rs 14000 grows to \(14000\times1.12^{2}=17561.6\), not Rs 15680.
Option (3) Rs 11200 — Incorrect. Rs 11200 grows to \(11200\times1.12^{2}=14049.28\), not Rs 15680.