What must Bill McGuire invest today to receive an annuity of $12,000 for four years semiannually at a 10% annual rate? All withdrawals will be made at the end of each period.

$77,558.55

Step-by-step explanation:

A fix periodic payment for specific period of time.

We need to calculate the present value annuity to determine the value of investment today.

Present value of annuity = P x ( 1 - ( 1 + r )^-n / r )

where

P = Periodic payment = $12,000

r = interest rate = 10% / 2 = 5%

n =numbers of payment = 4 years x 2 = 8 payments

Placing values in the formula

Investment Value today = $12,000 x ( 1 - ( 1 + 5% )^-8 / 5% )

Investment Value today = $77,558.55

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step-by-step explanation: