Question

A leasing contract calls for an immediate payment of $100,000 and nine subsequent $100,000 semiannual payments at six-month intervals. Assume the effective annual interest rate is 8%. (Hint: First calculate the semiannually compounded rate). What is the PV of these payments? (Do not round intermediate calculations. Round your answer to the nearest dollar amount.) Present value $ 846,081 correct

Answer 1

The PV of these payments is $843,533.

Step-by-step 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.