Question 64

Asum of moneyis doubled at some compoundinterest in 8 years. The numberofyears in which the amount becomes 4 times with samerate ofinterestis

Solution

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Let the principal be P, rate of interest be R, $$1+\frac{R}{100}=m$$ 
We are given that 2P = P*$$m^8$$ which gives us $$m^8=2$$

Now, let N be the number of years when sum of money becomes 4 times itself, hence:
$$4=m^N$$
$$2^2=m^N$$
$$\left(m^8\right)^2=m^N$$
Hence, N = 16 

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