find the amount of an annuity of $5000 payable at the end of each 3 months for 8 years,if money is worth 12% compounded quarterly.
To find the amount of an annuity, we can use the formula for the present value of an ordinary annuity:
PV = A * [(1 - (1 + r)^(-n)) / r]
where:
PV = present value of the annuity (amount of money today)
A = amount of each annuity payment
r = interest rate per period
n = number of periods
In this case, we need to find the present value of an annuity with payments of $5000, interest rate of 12% compounded quarterly, and a duration of 8 years.
First, we need to calculate the interest rate per period. Since the interest is compounded quarterly, we divide the annual interest rate by 4 (to get the quarterly rate):
Interest rate per period = 12% / 4 = 0.12 / 4 = 0.03 (or 3%)
Next, we calculate the number of periods. Since the annuity payments are made every 3 months and we have 8 years, we multiply the number of years by the number of periods per year (4 quarters):
Number of periods = 8 years * 4 quarters/year = 32 periods
Now, we can plug these values into the formula:
PV = $5000 * [(1 - (1 + 0.03)^(-32)) / 0.03]
Calculating the value:
PV = $5000 * [(1 - 1.03^(-32)) / 0.03]
Using a calculator:
PV ≈ $108,847.22
Therefore, the present value of the annuity is approximately $108,847.22.