James leases a ski chalet to his best friend, Janet. The lease term is five years with $20,000 annual payments due at the beginning of each year. What is the present value of the payments discounted at 8% per annum?

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Quizplus · Accepted Answer

The lease payments are an annuity due since payments are made at the beginning of each period. The present value of an annuity due can be calculated using the formula: $PV = PMT \times \left(\frac{1 - (1 + r)^{-n}}{r}\right) \times (1 + r)$, where PMT is the annual payment, r is the annual discount rate, and n is the total number of payments. Here, PMT = $20,000, r = 8% or 0.08, and n = 5. Plugging these values into the formula gives: $PV = $20,000 \times \left(\frac{1 - (1 + 0.08)^{-5}}{0.08}\right) \times (1 + 0.08) = $20,000 \times 4.31213 \approx $86,243$.

James Leases a Ski Chalet to His Best Friend, Janet