Final answer:
To calculate compound interest, use the formula A = P(1 + r/n)^(nt), where A is the total amount, P is the principal amount, r is the annual interest rate, t is the number of years, and n is the number of times interest is compounded per year. Plugging in the given values, the answer is approximately $680.89.
Step-by-step explanation:
To calculate compound interest, you can use the formula:
A = P(1 + r/n)^(nt)
Where:
- A is the total amount
- P is the principal amount (initial investment)
- r is the annual interest rate (in decimal form)
- t is the number of years
- n is the number of times interest is compounded per year
In this case, we have:
- P = $480
- r = 0.06 (6% expressed as a decimal)
- t = 6 years
- n = 4 (quarterly compounding)
Plugging in these values into the formula, we get:
A = $480(1 + 0.06/4)^(4*6)
A = $480(1.015)^24
A ≈ $680.89
Therefore, the answer is $680.89 (option b).