Final answer:
The present value of an annuity formula can be used to calculate the initial deposit needed to fund semiannual withdrawals of $700 for 9 years at a 5.4% interest rate compounded semiannually.
Step-by-step explanation:
To find the amount necessary to fund the given withdrawals, we can apply the formula for the present value of an annuity. Mathematically, this formula accounts for the semiannual withdrawals at a 5.4% interest rate that is compounded semiannually.
The present value of an annuity can be calculated using the formula:
PV = PMT ×
where PV is the present value of the annuity, PMT is the semiannual payment, r is the semiannual interest rate, and n is the total number of payments.
For the given scenario, we have:
PMT = $700
n = 9 years × 2 payments per year = 18 payments
r = 5.4% per year / 2 = 0.027 or 2.7% per period
Plugging these values into the formula we get:
PV = $700 ×
After solving the equation, you'll find the initial amount that must be deposited into the account to fund 18 semiannual withdrawals of $700 each at a 5.4% annual interest rate compounded semiannually.