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.)

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Business

Maia Norton

4 December, 08:03

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.)

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Mariana Travis · Answer 1

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

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