Question

your local auto store is willing to lease you a new car for $184 a month...

your local auto store is willing to lease you a new car for $184 a month for 38 months. payments are due on the first day of each month starting with the day you sign the lease. using an APR of 5.00% compounded semi-annually, what is the present value of the lease?
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Answer #1

Annual interest rate = 5.00% compounded semiannually

Semiannual interest rate = 5.00% / 2
Semiannual interest rate = 2.50%

Effective annual rate = (1 + Semiannual interest rate)^2 - 1
Effective annual rate = (1 + 0.0250)^2 - 1
Effective annual rate = 1.050625 - 1
Effective annual rate = 0.050625

Monthly interest rate = (1 + Effective annual rate)^(1/12) - 1
Monthly interest rate = (1 + 0.050625)^(1/12) - 1
Monthly interest rate = 1.00412392 - 1
Monthly interest rate = 0.00412392

Monthly payment = $184
Number of payments = 38

Payments are made at the beginning of each year

Present value = $184 + $184/1.00412392 + … + $184/1.00412392^36 + $184/1.00412392^37
Present value = $184 * 1.00412392 * (1 - (1/1.00412392)^38) / 0.00412392
Present value = $184 * 35.2501097
Present value = $6,486.02

Present value of the lease is $6,486.02 or $6,486

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