Final answer:
Using the compound interest formula, the investment of $3700 at an annual interest rate of 3.25%, compounded annually for 8 years, will grow to approximately $4782.79.
Step-by-step explanation:
To calculate the future value of a principal that is being compounded annually, we can use the compound interest formula: A = P(1 + r/n)nt, where A represents the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for.
In this scenario, the student has invested $3700 at an annual interest rate of 3.25% compounded annually for 8 years. We will use the formula to find the value of the investment after 8 years.
First, convert the interest rate from a percentage to a decimal by dividing by 100: 3.25% / 100 = 0.0325.
Next, since the interest is compounded annually, n will be 1. Now we can plug the values into the formula:
A = 3700(1 + 0.0325/1)1*8
When we calculate the exponent part:
1 + 0.0325 = 1.0325
Raising 1.0325 to the 8th power, we get approximately 1.2927.
Finally, multiply this result by the principal:
A = 3700 * 1.2927 ≈ $4782.79
Therefore, the investment will be worth approximately $4782.79 after 8 years.