Question

Find the amount and compound interest of ₹ 16000 in 1 year at 10% per annum compounded half-yearly.

Answer 1

Given:

• Principal (P) = ₹ 16000
• Rate of interest per annum (r) = 10%
• Time (t) = 1 year
• Compounded half-yearly means compound period is 6 months

Step-wise calculation:

1. Since interest is compounded half-yearly, the rate per half-year

= 10% ÷ 2

= 5%

2. Number of half-years in 1 year = 2

3. Amount `A = P xx (1 + (r//2)/100)^n`

`A = 16000 xx (1 + 5/100)^2`

`A = 16000 xx (105/100)^2`

Calculate:

`A = 16000 xx 105/100 xx 105/100`

A = 16000 × 1.05 × 1.05

A = 16000 × 1.1025

A = ₹ 17640

4. Compound Interest (C.I.) 

= Amount – Principal 

= ₹ 17640 – ₹ 16000 

= ₹ 1640