Question

Find the amount when ₹ 40000 is invested for `2 1/2` years at 8% per annum compounded yearly.

Answer 1

Given:

• Principal (P) = ₹ 40,000
• Rate of interest (R) = 8% per annum
• Time (T) = `2 1/2` years = 2.5 years
• Interest compounded yearly.

Step-wise calculation:

1. Amount after 1st year:

`A_1 = P xx (1 + R/100)`

`A_1 = 40000 xx (1 + 8/100)`

A₁ = 40000 × 1.08

A₁ = ₹ 43200

2. Amount after 2nd year:

A₂ = A₁ × 1.08

A₂ = 43200 × 1.08

A₂ = ₹ 46656

3. For the half year (0.5 year), the interest will be simple interest on the amount after 2 years, as compounding yearly means interest for full years only:

Simple Interest for 0.5 year:

`SI = A_2 xx R/100 xx 0.5`

`SI = 46656 xx 8/100 xx 0.5`

SI = 46656 × 0.04

SI = ₹ 1866.24

4. Total amount after 2.5 years:

A = A₂ + SI

A = 46656 + 1866.24

A = ₹ 48522.24

The amount when ₹ 40,000 is invested for `2 1/2` years at 8% per annum compounded yearly is ₹ 48522.24.