A sum of Rs \(x\) amounts to Rs 11979 in 2 years at 15% per annum when the interest is compounded every eight months. What is the value of \(x\)?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs 9000
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 in 2 years \(\displaystyle =\frac{24}{8}=3\)
\(x\times1.1^{3}=11979\), that is, \(1.331x=11979\)
\(\displaystyle x=\frac{11979}{1.331}=9000\)
The value of \(x\) is Rs 9000.