Multiple choice

Directions: Select the correct alternative from the given choices. If the principal at the beginning of the fifth year on a certain sum at a certain rate of interest, compounded annually, is 20% more than that at the beginning of the fourth year, then by what percent does the compound interest for the eleventh year exceed the compound interest for the eighth year?

  1. 44%

  2. 72.8%

  3. 69%

  4. 61.6%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Principal at start of year 5 is 1.2 * Principal at start of year 4, so rate r = 20% (0.2). CI for year n = P * (1+r)^(n-1) * r. CI for year 11 = P * (1.2)^10 * 0.2. CI for year 8 = P * (1.2)^7 * 0.2. Ratio = (1.2)^10 / (1.2)^7 = (1.2)^3 = 1.728. Increase = 72.8%.

AI explanation

Since the principal at the beginning of the fifth year is 20% more than at the beginning of the fourth year, the annual compound interest rate is 20%. The compound interest for any specific year equals 20% of the principal at the beginning of that year, so the interest for the eleventh year is 1.2 cubed times the interest for the eighth year. Calculating 1.728 minus 1 gives a 72.8% increase.

Keep practicing — related questions