The compound interest on a certain principal at the rate of 12.5% per annum, compounded annually, is Rs 1296 in the 3rd year. Find the principal.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Rs 8192
The interest of the 3rd year is earned on the amount at the end of the 2nd year. With 12.5% \(\displaystyle =\frac{1}{8}\), the amount grows by the factor \(\displaystyle \frac{9}{8}\) every year.
Amount after 2 years \(\displaystyle =P\times\frac{9}{8}\times\frac{9}{8}=\frac{81P}{64}\)
Interest in the 3rd year \(\displaystyle =\frac{1}{8}\times\frac{81P}{64}=\frac{81P}{512}\)
\(\displaystyle \frac{81P}{512}=1296\), so \(\displaystyle P=\frac{1296\times512}{81}=16\times512=8192\)
The principal is Rs 8192.