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A certain sum of money earns a simple interest of ₹ 800 over 2-year period. The same sum of money invested at the same rate of interest and same period on a compound interest basis earns an interest of ₹ 900. What is the sum?
Let the amount invested be 'P' and the rate of interest be 'r'.
Simple interest =$$\ \frac{\ P\times r\times2}{100}$$, which is equal to 800
=> $$\frac{\Pr}{100}=400$$
Compound interest = $$P\left(1+\frac{r}{100}\right)^2-P\ $$ = 900
$$P\left(\frac{r}{100}\right)^2+\frac{2\Pr}{100}=900$$
$$P\left(\frac{r}{100}\right)^2=100$$
$$400\left(\frac{r}{100}\right)=100$$
r = 25%
P = $$\frac{400\left(100\right)}{25}$$ = Rs 1600
The answer is option B.
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