Question 63

A certain sum invested on compound interest grows to ₹8,000 and ₹27,000 in three and six years, respectively when the interest is compounded annually. What is the percentage rate of interest?

Solution

A = $$P\left(1+\frac{r}{100}\right)^n$$

27000 = $$P\left(1+\frac{r}{100}\right)^6$$ ----------------I

8000 = $$P\left(1+\frac{r}{100}\right)^3$$ ------------II

Dividing I by II we get,

$$\frac{27}{8}=P\left(1+\frac{r}{100}\right)^3$$

$$\frac{3}{2}=1+\frac{r}{100}$$

$$\frac{r}{100}=\frac{1}{2}$$

$$r=50 %$$

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