Final answer:
To determine the amount of interest earned when a CD matures, use the formula for compound interest: A = P(1 + r/n)^(nt). Substituting the given values into the formula will give you the future value of the CD. Subtract the principal amount from the future value to find the interest earned.
Step-by-step explanation:
To determine the amount of interest you will have earned when the CD matures, you need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
P = principal amount (initial investment) = $18,000
r = annual interest rate (expressed as a decimal) = 0.0388
n = number of times that interest is compounded per year = 4 (quarterly)
t = number of years the money is invested for = 3
Using this formula, you can calculate the future value of the CD, which will give you the total amount of principal + interest:
A = 18000(1 + 0.0388/4)^(4*3)
Calculating the value, you will find that the CD will be worth approximately $19,964.46 at maturity. To determine the interest earned, subtract the principal amount:
Interest = $19,964.46 - $18,000 = $1964.46
Therefore, the amount of interest you will have earned when the CD matures is approximately $1964.46.