Final answer:
The final amount in Ray's savings account after 2 years with 4.5% interest compounded quarterly is approximately $656.
Step-by-step explanation:
To calculate the final amount in a savings account with compound interest, we can use the compound interest formula:
A = P(1 + rac{r}{n})^{nt}
Where:
- P is the principal amount (the initial amount of money)
- r is the annual interest rate (in decimal form)
- n is the number of times that interest is compounded per year
- t is the time the money is invested for, in years
In Ray's case:
- P = $600
- r = 4.5% or 0.045 (in decimal form)
- n = 4 (since the interest is compounded quarterly)
- t = 2 years
Thus, the formula becomes:
A = 600(1 + rac{0.045}{4})⁴
Let's calculate:
A = 600(1 + 0.01125)⁸
A = 600(1.01125)⁸
A ≈ 600(1.093443)
A ≈ $656
The final amount in the savings account after 2 years, rounded to the nearest dollar, is approximately $656.