Arun invests an amount of ₹4,000 at the rate of 2% simple interest per annum. For how many years did he invest the amount to double his sum?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 50 years
The sum doubles when the simple interest equals the principal. Simple interest \(\displaystyle=\frac{P\times R\times T}{100}\).
Interest needed \(=4000\) (to make ₹8,000)
Interest at 2% a year for \(T\) years must equal it: \(\displaystyle\frac{4000\times2\times T}{100}=4000\)
\(80T=4000\), so \(T=50\) years
Shortcut:
For any sum to double at simple interest, \(R\times T=100\), so \(\displaystyle T=\frac{100}{2}=50\) years; the amount ₹4,000 does not matter.