E9-21 Computing Present Value Involving Annuity and a Single Payment LO9-7 You h

Question

E9-21 Computing Present Value Involving Annuity and a Single Payment LO9-7 You have decided to buy a used car. The dealer has offered you two options: (FV of $1, PV of $1, FVA of $1, and PVA of $1) (use the appropriate factor(s) from the tables provided.) a. Pay $300 per month for 10 months and an additional $8,500 at the end of 10 months. The dealer is charging 24 percent per annum. b. When you buy the car, pay cash equal to the present value of the payments in option (a). Determine how much cash the dealer would charge in option (b). Present value

Explanation / Answer

Formula for present value of an anuuity = PV= A [ (1+k)n-1/k(1+k)n]

PV = Present value of fund

A = periodical (monthly) instalments=300

k=interest rate=24% pa=2% /month

n=periods=10 months

PV= 300[(1.02)10-1]/0.02(1.02)10

= 300*0.2190/0.02*1.2190=65.70/0.02438=2,694.83

So PV of installments=$2,694.83

PV of $8,500 at the end of 10 months = 8,500/1.20 (assuming 20% interest for 10 months)

=7,083.33

So Total PV of installments and payment = $(2,694.83+7,083.33)=$9,778.16

So dealer will charge $9,778.16 in option b.

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