Question

The compound interest of ₹ 28000 for 1 year at 10% per annum compounded half-yearly is ______.

Options

• ₹ 2680

• ₹ 2870

• ₹ 2920

• ₹ 3050

Answer 1

The compound interest of ₹ 28000 for 1 year at 10% per annum compounded half-yearly is ₹ 2870.

Explanation:

When the interest is compounded half-yearly, the yearly interest rate is divided by 2 and the number of compounding periods is doubled.

Here,

• Principal (P) = ₹ 28000
• Annual rate of interest (R) = 10%
• Time (T) = 1 year
• Compounded half-yearly means 2 periods in 1 year

Half-yearly rate = `10/2` = 5% 

Number of periods (n) = 1 × 2 = 2

Compound Interest formula for n periods:

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

Amount `A = 28000 xx (1 + 5/100)^2`

A = 28000 × (1.05)²

A = 28000 × 1.1025

A = 30870

Compound Interest = Amount – Principal

= 30870 – 28000

= ₹ 2870

Hence, the compound interest is ₹ 2870.