Final answer:
To calculate the interest earned in the fifth year on a $1,383 deposit at 7% interest compounded annually, use the compound interest formula with the given values and subtract the total amount after 4 years from the total amount after 5 years.
Step-by-step explanation:
To calculate the interest earned in year 5 on a $1,383 deposit that earns 7% interest compounded annually, we can use the formula for compound interest:
A = P(1 + r/n)^(nt) where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for, in years.
Since interest is compounded annually, n is 1. Therefore, the formula simplifies to A = P(1 + r)^t. To find the total amount after 5 years, we substitute P = $1,383, r = 0.07 (7% as a decimal), and t = 5 into the formula:
A = $1,383(1 + 0.07)^5
Calculate the total A, and then the interest earned is A - P. The specific interest for year 5 can be calculated by subtracting the total amount after 4 years from the total amount after 5 years.