Final answer:
The interest earned on a three-year CD for $26,000 at an APR of 3.7% compounded quarterly is approximately $4,483.39 when the CD matures.
Step-by-step explanation:
When you buy a three-year CD for $26,000 with an APR of 3.7% compounded quarterly you can determine the amount of interest earned when the CD matures by using the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- P is the principal amount ($26,000)
- r is the annual interest rate (3.7% or 0.037)
- n is the number of times interest is compounded per year (4 for quarterly)
- t is the number of years (3 years)
By plugging in the values, we get:
A = $26,000(1 + 0.037/4)^(4*3)
After calculating, the final amount A comes to approximately $30,483.39 when rounded to the nearest cent.
The interest earned is then the final amount minus the principal:
Interest Earned = Final Amount - Principal
Interest Earned = $30,483.39 - $26,000
Interest Earned = $4,483.39
Therefore, the interest earned on the CD after it matures is approximately $4,483.39.