Multiple choice

Lisa invests $5,000 into a savings account that earns 15% annual interest, compounded annually. What is the least number of full years required for her investment to more than double?

  1. 3 years

  2. 4 years

  3. 5 years

  4. 6 years

  5. 7 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To double the investment, the amount must reach at least $10,000. Using the formula A = P(1+r)^t, we solve 5000(1.15)^t > 10000, which simplifies to (1.15)^t > 2. Since 1.15^4 is approximately 1.75 and 1.15^5 is approximately 2.01, 5 years are required.

AI explanation

Using the compound interest formula A = P(1 + R/100)^n, we must find the least integer n where 5000(1.15)^n is greater than 10000. Testing the given years, for 4 years the amount is 5000(1.749) which equals 8745, but for 5 years the amount is 5000(2.011) which equals 10055. Since the investment first exceeds 10000 at 5 years, the least number of full years required is 5 years.

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