Gretta wants to retire in 13 years. At that time she wants to be able to withdraw $12,500 at the end of each 6 months for 7 years. Assume that money can be deposited at 8% per year compounded semiannually. What exact amount will Gretta need in 13 years?
To find the exact amount Gretta will need in 13 years, we can use the formula for the future value of an annuity. The future value of an annuity formula is given by:
FV = PMT * [(1 + r)^n - 1] / r
Where:
FV is the future value of the annuity,
PMT is the amount withdrawn at the end of each period,
r is the interest rate per period, and
n is the number of periods.
In this case, Gretta wants to withdraw $12,500 at the end of each 6 months for 7 years, which means she will withdraw a total of 2 * 7 = 14 times.
The interest rate per period is given as 8% per year compounded semiannually, so the interest rate per period is 8% / 2 = 4%.
Using the formula, we can calculate the future value of the annuity:
FV = $12,500 * [(1 + 0.04)^14 - 1] / 0.04
Simplifying this equation will give us the exact amount Gretta will need in 13 years.