Question:
Anil invests Rs. 22000 for 6 years in a certain scheme with 4% interest per annum, compounded half-yearly. Sunil invests in the same scheme for 5 years, and then reinvests the entire amount received at the end of 5 years for one year at 10% simple interest. If the amounts received by both at the end of 6 years are same, then the initial investment made by Sunil, in rupees, is
Anil invests Rs. 22000 for 6 years in a certain scheme with 4% interest per annum, compounded half-yearly. Sunil invests in the same scheme for 5 years, and then reinvests the entire amount received at the end of 5 years for one year at 10% simple interest. If the amounts received by both at the end of 6 years are same, then the initial investment made by Sunil, in rupees, is
Updated On: Jul 21, 2025
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Solution and Explanation
Anil invested \(22000\) for \(6\) years at \(4\%\) interest compounded half-yearly.
Amount = \(22000\left(1+\frac{2}{100}\right)^{12}\)
\(= 22000 \times (1.02)^{12}\)
Suppose, Sunil invests \(P\) rupees for \(5\) years at \(4\%\) C.I. half-yearly and \(10\%\) S.I. for \(1\) additional year.
Amount = \(P\left(1+\frac{2}{100}\right)^{10} \times 1.1\)
\(= P \times (1.02)^{10} \times 1.1\)
Given, both amounts are same,
\(22000 \times (1.02)^{12} = P \times (1.02)^{10} \times 1.1\)
\(P = \frac{22000 \times (1.02)^{12}}{(1.02)^{10} \times 1.1}\)
\(\Rightarrow P = \frac{22000 \times (1.02)^2}{1.1}\)
\(\Rightarrow P = 20808\)
So, the correct option is (C): \(20808\)
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