$1000 is invested at 8% interest compounded annually. $80 in interest is earned in the first year. Knowing that compound interest grows exponentially, how much interest is earned in the second year? Include dollars and cents in your answer.(1 point)

Question

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Answer 1

To calculate the interest earned in the second year on an investment of $1000 at an 8% annual interest rate compounded annually, we first determine the total amount in the account at the end of the first year.

1. Calculate the amount after the first year: \[ \text{Amount after Year 1} = \text{Principal} + \text{First Year Interest} \] \[ \text{First Year Interest} = \text{Principal} \times \text{Interest Rate} = 1000 \times 0.08 = 80 \] \[ \text{Amount after Year 1} = 1000 + 80 = 1080 \]

2. Calculate the interest earned in the second year: To find the interest earned in the second year, we apply the same interest rate to the new principal (the amount after the first year): \[ \text{Second Year Interest} = \text{Amount after Year 1} \times \text{Interest Rate} \] \[ \text{Second Year Interest} = 1080 \times 0.08 = 86.4 \]

Thus, the interest earned in the second year is \($86.40\).

Final answer: \[ \text{Interest earned in the second year: } $86.40 \]