Multiple choice

Anil invests Rs. 22,000 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

  1. 20,860

  2. 20,808

  3. 20,480

  4. 20,640
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Anil's amount = 22000 * (1 + 0.04/2)^(6*2) = 22000 * (1.02)^12. Sunil's amount is calculated based on 5 years of compound interest and 1 year of simple interest. Equating the two allows solving for the principal.

AI explanation

Using the compound interest formula for half-yearly compounding, Anil's final amount is 22000 * (1 + 0.02)^12 = 27917. For Sunil's initial investment of P, the amount after 5 years in the same scheme is P * (1.02)^10. Sunil reinvests this at 10% simple interest for one year, making his final amount P * (1.02)^10 * 1.10. Equating the final amounts gives P * (1.02)^10 * 1.10 = 27917, so P * 1.219 * 1.10 = 27917, which results in P = 20808 rupees.

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