Question: Jevon is a recent college graduate, and just landed a job. Still single, he plans to save his money…

Jevon is a recent college graduate, and just landed a job. Still single, he plans to save his money while he can, putting $8,721.08 away annually into an account that earns 3.29% interest, compounded annually. How much interest will he have earned by the time he gets married 3 years from now?

Solution

To calculate the interest Jevon will earn in 3 years from an account with annual compounding, we use the compound interest formula: \[ A = P(1 + r)^n \] where: - \( A \) is the amount of money accumulated after n years, including interest. - \( P \) is the principal amount (initial deposit). - \( r \) is the annual interest rate (decimal). - \( n \) is the number of years the money is invested for. First, we determine the parameters: \( P = 8721.08 \) \( r = \frac{3.29}{100} = 0.0329 \) \( n = 3 \) Now, substituting the values into the formula: \[ A = 8721.08(1 + 0.0329)^3 \] Calculate the compound factor: \[ 1 + 0.0329 = 1.0329 \] \[ (1.0329)^3 = 1.102298 \] Now, calculate \( A \): \[ A = 8721.08 \times 1.102298 = 9611.54 \] Find the interest earned by subtracting the principal from the total amount: \[ \text{Interest} = A - P = 9611.54 - 8721.08 = 890.46 \] The interest Jevon will have earned by the time he gets married in 3 years is $890.46.