Question

Suppose $10,000 was invested in a trust fund for a child at birth. After 20 years, the value of the fund is $27,126.40. Determine the interest rate the fund has been earning if interest has been compounded monthly. The interest rate is:

a. Less than 4%
b. Between 4% and 6%
c. Between 6% and 8%
d. Between 8% and 10%
e. More than 10%

Answer 1

To determine the interest rate the fund has been earning, we can use the formula for compound interest. By plugging in the given values, we find that the interest rate is less than 4%.

Step-by-step explanation:

To determine the interest rate the fund has been earning, we can use the formula for compound interest:

Final Amount = Principal * (1 + Interest Rate/number of compounding periods)^(number of compounding periods * time)

Given that $10,000 was invested and the final value after 20 years is $27,126.40, we can plug in these values to solve for the interest rate. The equation becomes:

$27,126.40 = $10,000 * (1 + r/12)^(12*20)

Simplifying and solving for r, we find that the interest rate is approximately 3.90%. Since this rate is less than 4%, the correct answer is: a. Less than 4%.