Question

A sum invested at compound interest amounts to ₹8,800 in 1 year and to ₹10,648 in 3 years. Calculate the rate percent and the sum.

• A. 10 and ₹ 8,000
• B. 12 and ₹ 5,000
• C. 10 and ₹ 6,000
• D. 12 and ₹ 8,000

Answer 1

The Correct Option is A

The problem involves compound interest, where we are given the amount after 1 year and the amount after 3 years. We need to determine the original sum (principal) \( P \) and the rate of interest \( R \% \).

Let's use the formula for compound interest:

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

First, for \( n = 1 \):

\( 8800 = P \left(1 + \frac{R}{100}\right) \)

This gives us:

\( P = \frac{8800}{1 + \frac{R}{100}} \)   &;(Equation 1)

Next, for \( n = 3 \):

\( 10648 = P \left(1 + \frac{R}{100}\right)^3 \)

Substitute the value of \( P \) from the first equation:

\( 10648 = \frac{8800}{1 + \frac{R}{100}} \left(1 + \frac{R}{100}\right)^3 \)

Simplifying further:

\( 10648 = 8800 \left(1 + \frac{R}{100}\right)^2 \)

Dividing both sides by 8800:

\( \frac{10648}{8800} = \left(1 + \frac{R}{100}\right)^2 \)

Calculating the left side:

\( 1.21 = \left(1 + \frac{R}{100}\right)^2 \)

Taking the square root of both sides:

\( 1.1 = 1 + \frac{R}{100} \)

Solving for \( R \):

\( \frac{R}{100} = 0.1 \)

\( R = 10 \) (Rate of Interest)

Substitute \( R = 10 \) back into Equation 1:

\( P = \frac{8800}{1.1} \)

Calculating the principal \( P \):

\( P = 8000 \)

Therefore, the rate percent is \( 10 \) and the sum invested is ₹8,000.