The rate of simple interest for first 2 years is 5%, for next 2 years is 7.5% and 10% for period beyond 4 years. If the Interest after 7 years is Rs. 4400. Find the compound interest on the same principal after 2 years at 10% interest rate, compounded annually.
Solution
Correct Answer: Option A
We know that, Simple Interest = (P × R × T)/100
Where, P = principal Amount, R = % Rate of interest, T = time period in years
Let the principle amount be Rs. x
∵ the interest rate is 5% per annum for first 2 years,
Simple Interest for first 2 years = (x × 5 × 2)/100 = x/10
∵ the interest rate is 7.5% per annum for next 2 years,
Simple Interest for next 2 years = (x × 7.5 × 2)/100 = 3x/20
Now, the time period remaining out of total time = 7 – (2 + 2) = 3 years
∵ the interest rate is 10% per annum for remaining 3 years,
Simple Interest for remaining 3 years = (x × 10 × 3)/100 = 3x/10
According to given information, total interest of 7 years = Rs. 4400
∴ 4400 = (x/10) + (3x/20) + (3x/10)
⇒ 4400 = 11x/20
⇒ x = (4400 × 20)/11
⇒ x = 8000
∴ the principal amount is Rs. 8000.
We know that, for compound interest is given by
\(\begin{array}{l} CI = P\;{\left( {1 + \frac{R}{{100}}} \right)^T} - P\\ \Rightarrow \;CI = 8000 \times {\left( {1 + \frac{{10}}{{100}}} \right)^2} - 8000\\ \Rightarrow CI = \;8000 \times \left( {\frac{{121}}{{100}} - 1} \right)\\ \Rightarrow CI = 8000 \times \frac{{21}}{{100}} = 1680 \end{array}\)
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