Multiple choice

Alison deposits $500 into a new savings account that earns 5 percent interest compounded annually. If Alison makes no additional deposits or withdrawals, how many years will it take for the amount in the account to double?

  1. 14

  2. 15

  3. 19

  4. 20
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the compound interest formula A = P(1 + r)^t, we want 2P = P(1.05)^t, so 2 = (1.05)^t. Using logarithms or estimation, 1.05^14 is approximately 1.98 and 1.05^15 is approximately 2.078. Therefore, it takes 15 years to exceed the doubling point.

AI explanation

To double the principal, the amount must become $1000, so using the compound interest formula we have 1000 = 500 * (1.05)^n. This simplifies to (1.05)^n = 2, and taking logarithms gives n = log(2) / log(1.05). Calculating this gives approximately 14.2 years, which rounds up to 15 years to fully double.

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