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Question 55
A certain sum at compound interest amounts to Rs.7800 for 5 years and for six years to ₹ 9048 (interest is compounded annually). What is the rate of interest?
Solution
Given, Amount for 5 years = Rs.7800
Amount for 6 years = Rs.9048
Then, Interest for 6th year = Rs.9048 - Rs.7800 = Rs.1248
Principal for 6th year = Rs.7800
Let the rate of interest be R%
$$7800 \times (1+\dfrac{R}{100}) = 9048$$
$$1+\dfrac{R}{100} = \dfrac{9048}{7800}$$
$$\dfrac{100+R}{100} = \dfrac{9048}{7800}$$
=> $$100+R = 116$$
=> R = 16%
Therefore, Rate of interest = 16%
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