If the interest on a sum of ₹y at 10% per annum compounded annually for 2 years is ₹462, then the total amount payable at the end of the two-year period will be _________.
₹2,662
The compound interest for 2 years at rate \(R = 10\%\) is a fixed fraction of the principal, so first find that fraction.
Amount after 2 years \(= P\left(1+\frac{10}{100}\right)^2 = P(1.1)^2 = 1.21P\).
Therefore compound interest \(= 1.21P - P = 0.21P\), i.e. 21% of the principal.
Given the interest is ₹462: \(0.21P = 462 \Rightarrow P = \frac{462}{0.21} = 2200\), so ₹y = ₹2,200.
Total amount payable = principal + interest \(= 2200 + 462 = 2662\).
Hence, the total amount payable at the end of two years is ₹2,662.
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Important Questions from Compound Interest
At what rate percent per annum will Rs. 7200 amount to Rs. 7938 in one year, if interest is compounded half yearly?
What is the compound interest (in Rs.) on a sum of Rs. 8192 for \(1 \frac{1}{4}\) years at 15% per annum, if interest is compounded 5-monthly ?
What is the difference (in Rs.) between the interests on Rs. 50,000 for one year at 8% per annum compounded half yearly and yearly?
A sum of money becomes Rs. 11,880 after 4 years and Rs. 17,820 after 6 years on compound interest, if the interest is compounded annually. What is the half of the sum (in Rs.)?
A sum invested at compound interest amounts to Rs. 7,800 in 3 years and Rs. 11,232 in 5 years. What is the rate per cent?
