Question

Amar invests some money at compound interest and finds that it will amount to ₹ 21,600 in 2 years and ₹ 31,104 in 4 years. Find the rate and the sum.

Answer 1

To find the rate and the sum from the given compound interest scenario, we can use the formula for compound interest:

`A = P(1 + r/100)^n`

Where:

• A is the amount after n years,
• P is the principal (initial investment),
• r is the rate of interest,
• n is the number of years.

From the problem, we have:

• The amount after 2 years is ₹ 21,600.
• The amount after 4 years is ₹ 31,104.

Let’s solve this step-by-step:

1. Let the principal amount be P and the rate be r.

2. The formula for compound interest gives:

`21600 = P(1 + r/100)^2`  ...(1)

`31104 = P(1 + r/100)^4`  ...(2)

3. Divide equation (2) by equation (1) to eliminate P:

`31104/21600 = (P(1 + r/100)^4)/(P(1 + r/100)^2)`

Simplifying:

`31104/21600 = (1 + r/100)^2`

`1.44 = (1 + r/100)^2`

4. Take the square root of both sides:

`sqrt(1.44) = 1 + r/100`

`1.2 = 1 + r/100`

5. Solve for r:

`r/100 = 0.2`

r = 20

Thus, the rate of interest is 20%.

6. Now substitute r = 20 into equation (1) to find P:

`21600 = P(1 + 20/100)^2`

`21600 = P(1.2)^2`

`21600 = P xx 1.44`

`P = 21600/1.44 = 15000`

Thus, the principal amount P is ₹ 15,000.