Question

A leasing contract calls for an immediate payment of $102,000 and nine subsequent $102,000 semiannual payments at six-month intervals. What is the PV of these payments if the annual discount rate is 10%? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

The PV of these payments if the annual discount rate is 10% is $826,997.84.

Step-by-step explanation:

The 10 fix payment in 5 year and paid immediately is example of annuity due to find its present value we will use following formula.

P = leasing payment = $102,000

Discount rate = r = 10% per year = 10% / 2 = 5% semiannually = 0.05

n = number of period = 10 semiannual periods

PV = P + P [ ( 1 - ( 1 + r )^-n-1) / r]

PV = 102,000 + 102,000 [ ( 1 - ( 1 + 0.05 )^-10-1) / 0.05]

PV = 102,000 + 102,000 [ ( 1 - ( 1.05 )^-9) / 0.05]

PV = 102,000 + 102,000 x 7.107822

PV = 102,000 + 724,997.84

PV = $826,997.84