A sum of money becomes 3 times in 10 years at the rate of compound interest (compounded annually). In how many years will it become 81 times?

40 years

The Formula that we used here is -

Amount = P$(1 \;+\; \frac{R}{100})^t$

3P = P [ 1 + \(\frac{R}{100}\) ]¹⁰

3 =  [ 1 + \(\frac{R}{100}\) ]¹⁰    ----(1)

ATQ,

81P = P [ 1 + \(\frac{R}{100}\) ]n

81 = [ 1 + \(\frac{R}{100}\) ]n

( 3 )4 =  [ 1 + \(\frac{R}{100}\) ]n

By using equation 1 ,

( [ 1 + \(\frac{15}{100}\) ]¹⁰ )4 = [ 1 + \(\frac{15}{100}\) ]ⁿ

So, n = 40 years

Hence, Sum become 81 times of itself in 40 years.