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

Question

Ramesh bought a mobile from a local store. He paid 1/6 of the price via UPI and 1/3 of the price via cash. He agreed to pay the balance amount a year later. While paying back the balance amount, Ramesh paid 10% interest on the balance amount. If the interest paid was Rs. 6000, what was the original price of the mobile?

Answer 1

Anil invested \(22000\) for \(6\) years at \(4\%\) interest compounded half-yearly. The calculated amount is \(22000\left(1+\frac{2}{100}\right)^{12}\), which simplifies to \(22000 \times (1.02)^{12}\).

Concurrently, Sunil invests \(P\) rupees for \(5\) years at \(4\%\) compound interest (C.I.) compounded half-yearly and \(10\%\) simple interest (S.I.) for \(1\) additional year. The resulting amount is \(P\left(1+\frac{2}{100}\right)^{10} \times 1.1\), which further simplifies to \(P \times (1.02)^{10} \times 1.1\).

Given that both calculated amounts are equal, the equation is \(22000 \times (1.02)^{12} = P \times (1.02)^{10} \times 1.1\).

Solving for \(P\), we get \(P = \frac{22000 \times (1.02)^{12}}{(1.02)^{10} \times 1.1}\), which reduces to \(P = \frac{22000 \times (1.02)^2}{1.1}\). This calculation yields \(P = 20808\).

Therefore, the correct option is (C): \(20808\).

Solution and Explanation

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