Multiple choice

Directions: Select the correct alternative from the given choices. If a certain sum, invested under compound interest, amounts to twice as much at the end of the seventh year as it would at the end of the second year, then the amount at the end of the 64th year will be how many times that at the end of the 49th year?

  1. 8

  2. 16

  3. 32

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

In compound interest, A = P(1+r)^n. A7 = P(1+r)^7, A2 = P(1+r)^2. A7 = 2 * A2 implies (1+r)^5 = 2. We want A64 / A49 = P(1+r)^64 / P(1+r)^49 = (1+r)^15 = ((1+r)^5)^3 = 2^3 = 8.

AI explanation

The amount at the end of the seventh year being twice that at the end of the second year means the money grows by a factor of 2 over a five year period. The duration between the 64th and 49th year is 15 years, which is exactly three of these five year periods. Therefore, the amount at the end of the 64th year will be 2 cubed, or 8, times the amount at the end of the 49th year.

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