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Find the amount in the account for the given principal, int P=$600,r=4%,t=9 years; compounded quarterly

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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.

User Michael Hancock
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