Determine the future value of an annuity due into which quarterly deposits of $450 are made for nine years if the annuity pays 10% compounded quarterly.
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To determine the future value of an annuity due, you can use the formula:
FV = P * ((1 + r)^n - 1) / r
where:
FV = Future Value
P = Periodic payment
r = Interest rate per period
n = Number of periods
In this case, the periodic payments are made quarterly with a deposit of $450, the interest rate is 10% per year compounded quarterly, and the annuity lasts for 9 years.
First, we need to convert the annual interest rate to a quarterly interest rate. Since the interest is compounded quarterly, the quarterly interest rate would be 10% divided by 4, which is 2.5% or 0.025 written as a decimal.
Next, we need to calculate the number of periods. Since the payments are made quarterly and the annuity lasts for 9 years, the number of periods would be 9 multiplied by 4, which is 36.
Now we can substitute the values into the formula:
FV = 450 * ((1 + 0.025)^36 - 1) / 0.025
Calculating the expression within the brackets first:
(1 + 0.025)^36 = 1.025^36 ≈ 1.949009
Substituting this value into the formula:
FV = 450 * (1.949009 - 1) / 0.025
≈ 450 * 0.949009 / 0.025
≈ 17,522.18
Therefore, the future value of the annuity due, considering quarterly payments of $450 for 9 years at an interest rate of 10% compounded quarterly, would be approximately $17,522.18.