Question

Find the amount and compound interest of ₹ 6250 at 16% per annum for 6 months, interest being compounded quarterly.

Answer 1

Given:

• Principal (P) = ₹ 6250
• Rate of interest per annum (R) = 16%
• Time (T) = 6 months = 0.5 years
• Interest compounded quarterly

Step-wise calculation:

1. Since interest is compounded quarterly, the rate per quarter = `16/4` = 4%.

2. Number of quarters n = 6 months = 2 quarters.

3. Amount formula for compound interest:

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

where R_q is the quarterly rate and n is the number of quarters.

4. Substitute values:

`A = 6250 xx (1 + 4/100)^2`

= 6250 × (1.04)²

= 6250 × 1.0816

= ₹ 6760

5. Compound Interest (CI)

= Amount – Principal 

= ₹ 6760 – ₹ 6250

= ₹ 510

The amount after 6 months is ₹ 6760 and the compound interest earned is ₹ 510.

This matches the example format and method for compound interest with quarterly compounding from the reference materials.