The compound interest on the sum of money at 8% p.a. for 2 years is more than the simple interest on the same sum at the same rate for the same time by Rs 76.80. Find the sum.

Answer: Rs 12,000

Solution:

According to the question,

Time (T) = 2 years

Rate of interest (R%) = 8% per annum

Difference between compound interest and simple interest (CI - SI) = Rs 76.80

Let the principal sum be represented by Rs P.

We have,

CI = $P \left [  \left ( 1 + \dfrac{R}{100} \right )^T - 1 \right ]$

$= P \left [ \left ( 1 + \dfrac{8}{100} \right )^2 - 1 \right ]$

$= P \left [ \left ( \dfrac{108}{100} \right )^2 - 1]$

$= P \left [ \left ( \dfrac{27}{25} \right )^2 - 1 \right ]$

$= P \left [ \dfrac{729}{625} - 1 \right ]$

$= P × \dfrac{729 - 625}{625}$

$= P × \dfrac{104}{625}$

$or, CI = \dfrac{104 P }{625}$

And,

SI = $\dfrac{P × T × R}{100}$

$= \dfrac{P × 2 × 8}{100}$

$or, SI = \dfrac{4P}{25}$

We know,

$CI - SI = 76.80$

$or, \dfrac{104P}{625} - \dfrac{4P}{25} = 76.80$

$or, \dfrac{104P - 4×25 P}{625} = 76.80$

$or, \dfrac{104 P - 100 P}{625} = 76.80$

$or, 4P = 76.80 × 625$

$or, 4P = 48000$

$or, 4 × P = 4 × 12000$

$\therefore P = Rs 12,000$

Hence, the required principal amount is Rs 12,000.