Final answer:
The question requires calculating the future value of an investment using compound interest formula. The total amount is found by converting the annual interest rate to a decimal, determining the number of compounding periods, and then applying these values into the compound interest formula.
Step-by-step explanation:
The student is asking for the future amount in an account with principal P=$600, an annual interest rate of r=4%, compounded quarterly over t=9 years. To calculate this, we will use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount ($600).
- 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 (9 years).
First, we need to convert the annual interest rate from a percentage to a decimal:
r = 4% = 0.04
Since the interest is compounded quarterly, there are 4 compounding periods per year:
n = 4
We can now plug the values into the formula:
A = 600(1 + 0.04/4)^(4*9)
A = 600(1 + 0.01)^(36)
A = 600(1.01)^36
To solve for A, we calculate (1.01)^36 and then multiply the result by 600. This will give us the total amount in the account after 9 years.
Compounding quarterly means that the interest is not just calculated on the principal each period, but also on the accumulated interest from previous periods, which can have a significant impact on the total amount over the time.