The Simple Interest on a certain sum at the rate of 5% per annum for 3 years is Rs.1260. Find the Compound Interest for that sum at the same rate and for the same period.

Simple Interest (SI) = Rs. 1260

Rate of Interest (R) = 5% per annum

Time (T) = 3 years

Simple Interest formula:

​$$SI = \frac{P \times R \times T}{100}$$​​

where:

P is the principal amount.

R is the rate of interest.

T is the time in years.

Compound Interest formula:

​$$CI = P \left(1 + \frac{R}{100}\right)^T - P$$​​

where:

CI is the compound interest.

calculating the principal using the simple interest formula:

​$$1260 = \frac{P \times 5 \times 3}{100} \\ \ \\1260 = \frac{15P}{100}\\ \ \\P = \frac{1260 \times 100}{15} = ₹8400$$​​

So, the principal P is ₹8400.

Now, the compound interest using the formula:

​$$CI = 8400 \left(1 + \frac{5}{100}\right)^3 – 8400 \\CI = 8400 \left(1.05\right)^3 – 8400 \\CI=8400×1.157625−8400 \\CI=9724.05−8400 \\CI= ₹1324.05$$ 

Therefore, Compound Interest is ₹ 1324.05 .   

Simple interest for 3 years = 1260

Simple interest for 1 year = 1260/3 = 420

5% of 420

=> 420 × (5/100)

=> 21

=> 5% of 21

=> 21 × (5/100)

=> 1.05

∴ Simple interest for 3 years = 3 × 420 + 3 × 21 + 1 × 1.05 = 1260 + 63 + 1.05 = 1324.05