Question

A man invests ₹ 8000 for 2 years at a certain rate of interest compound annually. At the end of first year, this sum amounts to ₹ 8640. Find

1. the rate of interest.
2. the amount at the end of second year.

Answer 1

Given:

• Principal, (P = ₹ 8000)
• Time for first year, (T = 1) year
• Amount at the end of first year, (A = ₹ 8640)
• Total time = 2 years (compound interest, compounded annually)

Step-wise calculation:

Step 1: Find the rate of interest (R)

Using the compound interest formula for the first year:

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

Substitute given values:

`8640 = 8000 xx (1 + R/100)`

Divide both sides by 8000:

`8640/8000 = 1 + R/100`

`1.08 = 1 + R/100`

Subtract 1 from both sides:

`0.08 = R/100`

Multiply both sides by 100:

R = 8%

Step 2: Find the amount at the end of second year

For the second year, the principal becomes the amount at the end of the first year:

P = 8640, R = 8%, T = 1 year

The amount after the second year is:

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

= `8640 xx (1 + 8/100)`

= 8640 × 1.08

= ₹ 9331.20