Find the compound interest on ₹64000 at 10% per annum for 9 months when interest is compounded quarterly.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → ₹4921
When interest is compounded quarterly, the yearly rate is divided by 4 and each quarter counts as one period.
Rate per quarter \(=10\%\div4=2.5\%\); number of quarters in 9 months \(=3\)
Amount \(\displaystyle =64000\times\left(1+\frac{2.5}{100}\right)^{3}=64000\times\left(\frac{41}{40}\right)^{3}\)
\(64000=40^{3}\), so Amount \(=41^{3}=68921\)
Compound interest \(=68921-64000=4921\)
Tip: Write the growth factor as a fraction (2.5% gives \(\frac{41}{40}\), 5% gives \(\frac{21}{20}\), 10% gives \(\frac{11}{10}\)); question setters often choose a principal that is a power of the denominator, and the amount then comes out without long multiplication.