Find the compound interest at the rate of 5 % per annum for 3 years on that principal which in 3 years at the rate of 5 % per annum gives Rs 1200 as simple interest.

Given :

For compound interest:

Rate of interest (R)$=5$%.

Time (N)$=3$ years.

For simple interest:

Rate of interest (R)$=5$%.

Time (N)$=3$ years.

Simple interest (SI)$=1200$.

To do :

We have to find the principal(P) and compound interest(CI).

Solution :

We know that,

$SI = \frac{PNR}{100}$

$1200 = \frac{P \times 3 \times 5}{100}$

$P = \frac{1200 \times 100}{3 \times 5}$

 $P = 400 \times 20$

$P = 8000$

The principal is ₹8000.

$CI = P(1+\frac{R}{100})^N - P$

$CI =8000 (1+ \frac{5}{100})^3 - 8000$

$CI = 8000 (\frac{100+5}{100})^3 -8000$

$CI = 8000 (\frac{105}{100})^3 -8000$

$CI = 8000 (\frac{21}{20})^3 - 8000$

$CI = 8000 \times \frac{9261}{8000} - 8000$

$CI = 9261 - 8000 = 1261$

Therefore, the Compound interest is ₹1261.