Question

A man invests ₹ 10000 for 3 years at a certain rate of interest compounded annually. At the end of first year, this sum amounts to ₹ 11000. Find

1. the rate of interest. 
2. the compound interest for 3 years.

Answer 1

Given:

• Principal (P = ₹ 10000)
• Time (T = 3) years
• Amount at the end of 1st year ( A₁ = ₹ 11000)
• Interest is compounded annually

Step 1: Find the rate of interest

The amount after 1 year is given by the compound interest formula:

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

Substitute the values:

`11000 = 10000 xx (1 + R/100)`

Divide both sides by 10000:

`1 + R/100 = (11000)/(10000)`

`1 + R/100 = 1.1`

Subtract 1 on both sides:

`R/100 = 0.1`

Multiply both sides by 100:

R = 10%

Rate of interest is 10% per annum.

Step 2: Find the compound interest for 3 years

Now, to find the amount after 3 years:

`A_3 = P xx (1 + R/100)^3`

A₃ = 10000 × (1.1)³

Calculate:

(1.1)³ = 1.331

So, A₃ = 10000 × 1.331 = ₹ 13310

Compound Interest (C.I.)

= Amount after 3 years – Principal

C.I. = 13310 – 10000

C.I. = ₹ 3310