Anil invests Rs 22000 for 6 years in a scheme with 4% interest per annum, compounded half-yearly. Separately, Sunil invests a certain amount in the same scheme for 5 years, and then reinvests the entire amount he receives 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 equal, then the initial investment, in rupees, made by Sunil 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's Investment: Principal = Rs 22000. Interest Rate = 4% per year, compounded half-yearly (2% per half-year). Time = 6 years (12 half-years). The formula for the final amount is:

Amount = Principal × $(1 + \frac{Rate}{100})^{Time}$Nbsp;

Substituting the values:

Amount = 22000 × $(1 + \frac{2}{100})^{12}$ ≈ 27816.22

Sunil's Investment: Let the initial investment be P. After 5 years at 4% compounded half-yearly, the amount is:

This amount is then reinvested for 1 year at 10% simple interest. The final amount for Sunil is: $P \left( 1 + \frac{2}{100} \right)^{10} \left( 1 + \frac{10}{100} \right)$

Since both amounts are equal: $27816.22 = P \left( 1 + \frac{2}{100} \right)^{10} \left( 1 + \frac{10}{100} \right)$

Solving for P, we find $P \approx 20808$.

Therefore, Sunil's initial investment was approximately Rs 20808.

The Correct Option is B

Solution and Explanation

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