Question

You are planning to buy a luxurious car. The retail price of the car is $65,000. Fox Auto is making you the following offer: You pay $10,000 down and then $2,000 a month for next 30 months. The APR is 12 percent (compounded monthly). This offer is equivalent to a _____ off the retail price (when paid in cash today).

Answer 1

PV of CFs: CF * PVF(r%, n)

r is int Rate and n is time period

Month	CF	PVF @1%	Disc CF
0	$ 10,000.00	1.0000	$ 10,000.00
1	$   2,000.00	0.9901	$   1,980.20
2	$   2,000.00	0.9803	$   1,960.59
3	$   2,000.00	0.9706	$   1,941.18
4	$   2,000.00	0.9610	$   1,921.96
5	$   2,000.00	0.9515	$   1,902.93
6	$   2,000.00	0.9420	$   1,884.09
7	$   2,000.00	0.9327	$   1,865.44
8	$   2,000.00	0.9235	$   1,846.97
9	$   2,000.00	0.9143	$   1,828.68
10	$   2,000.00	0.9053	$   1,810.57
11	$   2,000.00	0.8963	$   1,792.65
12	$   2,000.00	0.8874	$   1,774.90
13	$   2,000.00	0.8787	$   1,757.33
14	$   2,000.00	0.8700	$   1,739.93
15	$   2,000.00	0.8613	$   1,722.70
16	$   2,000.00	0.8528	$   1,705.64
17	$   2,000.00	0.8444	$   1,688.75
18	$   2,000.00	0.8360	$   1,672.03
19	$   2,000.00	0.8277	$   1,655.48
20	$   2,000.00	0.8195	$   1,639.09
21	$   2,000.00	0.8114	$   1,622.86
22	$   2,000.00	0.8034	$   1,606.79
23	$   2,000.00	0.7954	$   1,590.88
24	$   2,000.00	0.7876	$   1,575.13
25	$   2,000.00	0.7798	$   1,559.54
26	$   2,000.00	0.7720	$   1,544.10
27	$   2,000.00	0.7644	$   1,528.81
28	$   2,000.00	0.7568	$   1,513.67
29	$   2,000.00	0.7493	$   1,498.68
30	$   2,000.00	0.7419	$   1,483.85
PV of CFs			$61,615.42

offer = Retail Price - PV of CFs

= $ 65,000 - $ 61615.42

= $ 3384.58

Offerin % = Offer amount / Retail price

= 3384.58 / 65000

= 0.0521 i.e 5.21%