A sum of ₹1500 is invested at 5% p.a. simple interest. If the interest is added to the principal after every 10 years, the amount will become ₹3000 after:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(16\displaystyle\frac{2}{3}\) years
Simple interest is earned only on the principal of the period. When the interest is added to the principal after 10 years, the second period earns interest on the new, larger principal.
The first 10 years (principal ₹1500):
Interest \(\displaystyle =\frac{1500\times5\times10}{100}=\) ₹750
Amount \(=1500+750=\) ₹2250, the new principal
After that (principal ₹2250, ₹750 more needed to reach ₹3000):
Interest per year \(\displaystyle =\frac{2250\times5}{100}=\) ₹112.50
Time \(\displaystyle =\frac{750}{112.5}=6\frac{2}{3}\) years
Total time \(\displaystyle =10+6\frac{2}{3}=16\frac{2}{3}\) years.