If the compound interest on a certain sum of money for 3 years at 5% per annum is ₹3,783, then what would be the simple interest on the same sum of money for the same period and at the same rate?

Correct option is A

Given:

Compound Interest (CI) for 3 years at 5% per annum = ₹3,783

Rate of interest = 5% per annum

Time = 3 years

Formula Used:
The formula for compound interest is:

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

Where:

A is the amount after interest.

P is the principal amount.

R is the rate of interest per year.

T is the time in years.

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

compound interest (CI) = A - P

Solution:

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

3,783 = $$P \left(1 + \frac{5}{100}\right)^3 - P$$​

3,783 = $$P \left(1.05\right)^3 - P$$​​

3,783 = P(1.157625 - 1)

3,783 $$= P \times 0.157625$$​​

P = $$\frac{3,783}{0.157625} = 24,000$$​​

Substituting the values P = 24,000, R = 5, and T = 3:

SI =$$\frac{24,000 \times 5 \times 3}{100} = \frac{360,000}{100} = 3,600$$​

Thus, the simple interest on the same sum of money for the same period at the same rate is ₹3,600.

Alternate Method:

5% = $$\frac1{20}$$

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