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 50 years 35 years 30 years |
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. |