Final answer:
Compound interest is an interest rate calculation on the principal plus the accumulated interest. To calculate compound interest, use the formula A = P(1 + r/n)^(n*t), where A is the total amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, the total amount with compound interest is $4,577.17 and the interest earned is $77.17.
Step-by-step explanation:
Compound interest is an interest rate calculation on the principal plus the accumulated interest. It is different from simple interest, which is calculated only on the principal amount. To calculate compound interest, we can use the formula:
A = P(1 + r/n)^(n*t)
Where:
- A is the total amount after the interest has compounded for a certain period of time
- P is the principal amount
- r is the annual interest rate
- n is the number of times the interest is compounded per year
- t is the number of years
In your case, you have an annual interest rate of 5%, a principal amount of $4,500, and a time period of 1 year. Since the interest is compounded quarterly, we need to adjust the formula accordingly:
A = $4,500(1 + 0.05/4)^(4*1) = $4,500(1.0125)^4 = $4,577.17
The amount earned through compound interest is therefore $4,577.17 - $4,500 = $77.17.