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?
Answer & explanation
Correct answer: option 1
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.