Multiple choice

Priya invests Rs. 160,000 in a financial plan that offers 20% annual interest, compounded quarterly, for a period of 4 years. Meanwhile, Karan invests a certain sum in the same plan for 3 years and then reinvests the amount he receives at the end of 3 years into a scheme offering simple interest at 8% per annum for 1 additional years. If both Priya and Karan receive equal total amounts at the end of 4 years, what was the initial amount invested by Karan?

  1. Rs. 183,250

  2. Rs. 180,075

  3. Rs. 182,430

  4. Rs. 212,790
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Priya's amount: 160000 * (1 + 0.20/4)^(4*4) = 160000 * (1.05)^16 = 348250.8. Let Karan's investment be P. After 3 years at 20% compounded quarterly: P * (1.05)^12. Then simple interest for 1 year at 8%: [P * (1.05)^12] * 1.08 = 348250.8. Solving for P gives approx 180075.

AI explanation

Priya invests Rs. 160,000 at 20% annual interest compounded quarterly for 4 years, so her final amount is 160000 multiplied by (1 + 0.20/4) raised to the power of 16, which is 160000 multiplied by 1.05^16. Karan invests in the same plan for 3 years, so his amount after 3 years is P multiplied by 1.05^12, and he reinvests this at 8% simple interest for 1 year to get an amount of P multiplied by 1.05^12 multiplied by 1.08. Equating the two final amounts gives P multiplied by 1.05^12 multiplied by 1.08 equals 160000 multiplied by 1.05^16, which simplifies to P equals 160000 multiplied by 1.05^4 divided by 1.08. Calculating 1.05^4 as approximately 1.2155, we get P equal to approximately 194480 divided by 1.08, which is Rs. 180,075.

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