[Solved] Rs. 1000 doubled in 10 years when compounded annually. (2024)

Calculation:

According to the question:

Rs. 1000 invested in compound interest becomes Rs. 2000 in 10years

The amount will double again in another 10 years.

So, the amount will become Rs. 4000 in another 10 years.

To earn another Rs. 2000 interest, it will take another 10 years

∴ The answer will be 10 years.

Alternate Method

Given:Rs. 1000 doubles in 10years when compounded annually.

To Find:How many more years will it take to get another Rs. 2000 compound interest?

Formula :A = p (1 + r/100)t

Calculation:

Amount after 10years (A) = 2 × 1000 = Rs. 2000

Let the rate of interest be r

A = p (1 + r/100)t

2000 = 1000 (1 + r/100)10

2000/1000 = (1 + r/100)10

2 =(1 + r/100)10_____ (1)

Now, we need to find the time it will take for Rs. 2000 compound interest on this amount.

Let the time be tyears

Hence, the new amount will beA = 2000 + 2000 = Rs. 4000

Also, P = Rs. 2000 and the rate of interest be r

A = p (1 + r/100)t

4000 = 2000 (1 + r/100)t

4000/2000 = (1 + r/100)t

2 =(1 + r/100)t_____ (2)

From (1) and (2)

(1 + r/100)t=(1 + r/100)10

Hence, t = 10

∴It will take another 10years to get another compound interest of Rs. 2000.