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If $15,000 is invested at 6.5% annual interest compounded annually, how long would it take for the account balance to reach $50,000?

a. 19.1 years
b. 22.5 years
c. 17.3 years
d. 25.9 years

1 Answer

5 votes

Final answer:

To find out how long it takes for $15,000 to grow to $50,000 at 6.5% annual interest compounded annually, we use the compound interest formula. After substituting the values and solving for time, we discover it takes approximately 22.5 years.

Step-by-step explanation:

To calculate the time needed for an investment to grow from $15,000 to $50,000 at an annual interest rate of 6.5%, compounded annually, we use the formula for compound interest:


A = P(1 + r/n)(nt)

Where:

  • A is the amount of money accumulated after n years, including interest.
  • P is the principal amount (the initial amount of money).
  • r is the annual interest rate (decimal).
  • n is the number of times that interest is compounded per year.
  • t is the time the money is invested for in years.

Given that the interest is compounded annually, n = 1. We want to find t when A = $50,000, P = $15,000, and r = 0.065 (6.5%).

Substituting the values into the formula and solving for t, we get:

$50,000 = $15,000(1 + 0.065)t

We can rewrite this equation as:

3.3333 = (1.065)t

Using logarithms to solve for t:

t = log(3.3333) / log(1.065)

Calculating this gives us t ≈ 22.5 years.

Therefore, it would take approximately 22.5 years for the investment to grow to $50,000, making the correct answer b. 22.5 years.

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