Multiple choice

Ram plans to allocate $40,000 into two investment options, X and Y. He decides to invest half of the amount in option X, which offers a compound interest rate of 20% per year for two years. The remaining amount is invested in option Y, which provides a simple interest rate that is 2% higher than the rate of option X for the same duration. Quantity A Compound interest earned from investment option X after two years Quantity B Simple interest earned from investment option Y after two years

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Option X: 20000 at 20% compound interest for 2 years = 20000 * (1.2^2 - 1) = 20000 * 0.44 = 8800. Option Y: 20000 at 22% simple interest for 2 years = 20000 * 0.22 * 2 = 8800. Both are equal.

AI explanation

Ram invests half of the 40000, which is 20000, into option X at a compound interest rate of 20% for two years. The compound interest formula gives an amount of 20000 multiplied by 1.20 squared, which equals 28800, meaning the interest for option X is 8800. The simple interest rate for option Y is 2% higher than 20%, so it is 22%. Using the simple interest formula for the 20000 in option Y, the interest is 20000 multiplied by 0.22 multiplied by 2, which equals 8800. Both quantities are 8800, meaning the two quantities are equal.

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