Find the compound interest on Rs. 1000 for 10 years at 4% per annum if the interest is calculated quarterly.​

The compound interest is approximately Rs. 488.46.

To determine the compound interest on Rs. 1000 over a period of 10 years at an annual interest rate of 4%, compounded quarterly, we will follow a structured approach using the compound interest formula.

1. Identify the variables in the formula. The formula for compound interest is given by A = P(1 + r/n)^{nt}, where:

A represents the future value of the investment,

2. P is the principal amount, which is Rs. 1000,

3. r is the annual interest rate expressed as a decimal (4% or 0.04),

4. n is the number of times interest is compounded per year (quarterly compounding means n = 4),

5. t is the number of years the money is invested (10 years).

6. Substitute the identified values into the formula. We have:

A = 1000(1 + 0.04/4)^{4*10}.

7. Simplify the expression inside the parentheses. This becomes:

A = 1000(1 + 0.01)^{40}.

8. Calculate the value of (1 + 0.01)^{40}. This results in:

A = 1000(1.01)^{40}.

9. Use a calculator to find (1.01)^{40}, which is approximately 1.488864. Thus, we have:

A ≈ 1000 * 1.488864.

10. Calculate the future value A:

A ≈ 1488.864.

11. Finally, calculate the compound interest (CI) by subtracting the principal from the future value:

CI = A - P = 1488.864 - 1000 = 488.864.

Therefore, the compound interest on Rs. 1000 for 10 years at 4% per annum, compounded quarterly, is approximately Rs. 488.46.