Multiple choice

Anita invested a portion of her savings in a bond with a simple interest rate, and the rest in a savings account with compound interest. The simple interest investment grew to Rs. 9,600 after 4 years with an annual interest rate of 7%. Simultaneously, the compound interest investment, compounded annually at a rate of 10%, grew to Rs. 7,986 after the same period of 3 years. Determine the total amount Anita initially invested in both investments.

  1. Rs. 12,500

  2. Rs. 13,500

  3. Rs. 13,800

  4. Rs. 14,500

  5. Rs. 15,200
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Simple interest: P1 * (1 + 0.07 * 4) = 9600 => P1 * 1.28 = 9600 => P1 = 7500. Compound interest: P2 * (1 + 0.10)^3 = 7986 => P2 * 1.331 = 7986 => P2 = 6000. Total = 7500 + 6000 = 13500.

AI explanation

For the first investment, the simple interest formula gives the principal as the total amount divided by (1 plus the rate multiplied by the time), which is 9600 divided by 1.28, resulting in Rs. 7,500. For the second investment, the compound interest formula gives the principal as 7986 divided by 1.10 raised to the power of 3, which evaluates to Rs. 6,000. Adding the two initial principals of 7500 and 6000 gives a total initial investment of Rs. 13,500.

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