Answer:
The PV of these payments is $843,533.
Explanation:
The present value (PV) of the $100,000 immediate payment = $100,000
To calculate the PV of the nine subsequent $100,000 semiannual payments, the formula for calculating the present value of an ordinary annuity is used as follows:
PV = P * [{1 - [1 / (1 + r)]^n} / r] …………………………………. (1)
Where;
PV = Present value of the nine subsequent $100,000 semiannual payments =?
P = Semiannual payments = $100,000
r = effective semiannual interest = 8% / 2 = 4%, or 0.04
n = number of semi-annuals = 9
Substitute the values into equation (1) to have:
PV = $100,000 * ((1 - (1 / (1 + 0.04))^9) / 0.04)
PV = $100,000 * ((1 - (1 / 1.04)^9} / 0.04)
PV = $100,000 * ((1 - 0.961538461538461^9) / 0.04)
PV = $100,000 * ((1 - 0.702586735578828) / 0.04)
PV = $100,000 * (0.297413264421172 / 0.04)
PV = $100,000 * 7.4353316105293
PV = $743,533
To calculate the PV of these payments, we have:
PV of these payments = PV + The present value (PV) of the $100,000 immediate payment = $743,533 + $100,000 = $843,533
Therefore, the PV of these payments is $843,533.
