A sum of money becomes 3 times in 10 years at the rate of compoundinterest (compounded annually). In how many years will it become 81 times?
amount with compound interest = $$P(1+\frac{R}{100})^n$$
3P= $$P(1+\frac{R}{100})^{10} $$
3= $$(1+\frac{R}{100})^{10}$$Â Â ->( 1)
amount with compound interest = $$P(1+\frac{R}{100})^n$$
81P= $$P(1+\frac{R}{100})^T$$
$$3^4$$ =$$(1+\frac{R}{100})^T$$Â Â ->( 2)
Equating both the equations
$$((1+\frac{R}{100})^ {10})^4$$ =$$(1+\frac{R}{100})^T$$
T = 40 years
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