Multiple choice

An investor deposits Rs. 1,500 in an account earning interest compounded annually at r%. He withdraws Rs. 720 at the end of the first year and Rs. 972 at the end of the second year. After the second withdrawal, the balance becomes zero. Find r.

  1. 6

  2. 7

  3. 8

  4. 9
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Year 1: 1500(1+r/100) - 720 = Balance. Year 2: Balance(1+r/100) - 972 = 0. Let x = 1+r/100. 1500x - 720 = B. (1500x - 720)x = 972. 1500x^2 - 720x - 972 = 0. Divide by 12: 125x^2 - 60x - 81 = 0. Using quadratic formula: x = [60 +/- sqrt(3600 - 4*125*-81)] / 250 = [60 +/- sqrt(3600 + 40500)] / 250 = [60 +/- sqrt(44100)] / 250 = [60 + 210] / 250 = 270/250 = 1.08. r = 8%.

AI explanation

Using the compound interest formula, the balance after the first year is 1500 times 1 plus r divided by 100 minus 720. At the end of the second year, this entire balance multiplies by 1 plus r divided by 100 again, and withdrawing 972 brings it to zero. Setting up the equation: 1500 times 1 plus r divided by 100 minus 720 times 1 plus r divided by 100 equals 972, we find that 1 plus r divided by 100 equals 1.08. Solving for r gives r equals 8.

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