Question
A certain some of money and Rs. 2420 in 2 years and Rs. 2662 in 3 years at same rate of compound interest, compounded annually. The rate of interest per annum is = ?
Answer: Option D
$$\eqalign{
& {\text{Amount after three years}} \cr
& {\text{ = Rs. 2662}} \cr
& {\text{Amount after two years}} \cr
& {\text{ = Rs. 2420}} \cr
& {\text{Net interest earned in the }}{{\text{3}}^{{\text{rd}}}}{\text{ year}} \cr
& {\text{ = }}\,{\text{2662}} - {\text{2420}} \cr
& {\text{ = Rs}}{\text{. 242}} \cr
& {\text{Rate of interest (r)}} \cr
& {\text{ = }}\frac{{242}}{{2420}} \times {\text{100 = 10% }} \cr} $$
(∴ 2nd year's amount is principal for 3rd year)
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$$\eqalign{
& {\text{Amount after three years}} \cr
& {\text{ = Rs. 2662}} \cr
& {\text{Amount after two years}} \cr
& {\text{ = Rs. 2420}} \cr
& {\text{Net interest earned in the }}{{\text{3}}^{{\text{rd}}}}{\text{ year}} \cr
& {\text{ = }}\,{\text{2662}} - {\text{2420}} \cr
& {\text{ = Rs}}{\text{. 242}} \cr
& {\text{Rate of interest (r)}} \cr
& {\text{ = }}\frac{{242}}{{2420}} \times {\text{100 = 10% }} \cr} $$
(∴ 2nd year's amount is principal for 3rd year)
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