Question

You’re looking to buy a 2018 Ford Fusion Titanium with sunroof and leather seats at a price of $32,000. Being a poor college student, you have cash to pay taxes, title, license & fees but your parents offer to give you 10% of the price, $3200, as a down payment and you need to finance the remainder of $28,800. You smartly researched your finance options and got pre-approval at a 3.3% APR for 60 months on your own so you’re not at the mercy at depending on financing from the car dealership. Ford is offering 0% APR financing or $2,750 cash back which would be used as an additional down payment that reduce that amount that you would need to finance. You would use your 3.3% APR pre-approved financing if you elect the $2750 cash back option. Answer the following questions.

3. At what APR would you be indifferent between the two offers? In other words, at what APR would you have the same monthly payment (assuming a 60-month loan term) for the $2750 cash back offer as you would with the 0% APR financing offer?

4. Let’s assume you go with the offer in question #2 (What would be your monthly car loan payment under the Ford’s $2,750 cash back offer and your 3.3% APR pre-approved financing (assume a 60-month loan term)? . Construct an amortization schedule for the loan for all 60 monthly payments. What is your loan balance after 36 months?

Answer 1

In the given problem, you would like to buy Ford Fusion Titanium with sunroof and leather seats at a price of $32,000

You can able to finance 10% of the price $32,000, $3200

The remaining $28,800 you need to finance and you got pre-approval finance at 3.30% APR for 60 months.

As per the above mentioned finance amount of $28,800, the Equated Monthly Instalment (EMI) may be calculated by using the following formula,

Where,

EMI = Equated Monthly Instalment

P = Principal Amount

r =  rate of interest calualted in monthly basis (3.3/100/12)

n = tenture in number of months (60 Months)

EMI = $28,800*0.00275*(1+0.00275)^60/((1+.00275)^60 - 1)

EMI = $521

Now, Ford is offering two offers,

Offer#1: 0% APR Financing

Offer#2: $2,750 cash back which would be used as an additional down payment

As per offer#1 the EMI would be $480 ($28,800/60)

As per offer#2 the EMI will be $472 (As a cash back offer by Ford $2750 can be used as down payment, hence the loan amount would be $26,050 ($28,800-$2750)

EMI = $26, 050*0.00275*(1+0.00275)^60/((1+.00275)^60 - 1)

EMI = $472

Loan Amortization Schedule for 60 Month Payments (Amount $)

MONTHS	EMI	INTEREST	PRINCIPAL REPAYMENT	OUTSTANDING PRINCIPAL
0				26,050
1	472	72	400	25,650
2	472	71	401	25,249
3	472	69	402	24,847
4	472	68	403	24,444
5	472	67	404	24,039
6	472	66	405	23,634
7	472	65	407	23,227
8	472	64	408	22,820
9	472	63	409	22,411
10	472	62	410	22,001
11	472	61	411	21,590
12	472	59	412	21,178
13	472	58	413	20,764
14	472	57	414	20,350
15	472	56	416	19,934
16	472	55	417	19,517
17	472	54	418	19,100
18	472	53	419	18,681
19	472	51	420	18,260
20	472	50	421	17,839
21	472	49	423	17,416
22	472	48	424	16,993
23	472	47	425	16,568
24	472	46	426	16,142
25	472	44	427	15,715
26	472	43	428	15,286
27	472	42	430	14,857
28	472	41	431	14,426
29	472	40	432	13,994
30	472	38	433	13,561
31	472	37	434	13,127
32	472	36	435	12,692
33	472	35	437	12,255
34	472	34	438	11,817
35	472	32	439	11,378
36	472	31	440	10,938
37	472	30	441	10,496
38	472	29	443	10,053
39	472	28	444	9,610
40	472	26	445	9,164
41	472	25	446	8,718
42	472	24	448	8,270
43	472	23	449	7,822
44	472	22	450	7,372
45	472	20	451	6,920
46	472	19	453	6,468
47	472	18	454	6,014
48	472	17	455	5,559
49	472	15	456	5,103
50	472	14	458	4,645
51	472	13	459	4,186
52	472	12	460	3,726
53	472	10	461	3,265
54	472	9	463	2,802
55	472	8	464	2,338
56	472	6	465	1,873
57	472	5	466	1,407
58	472	4	468	939
59	472	3	469	470
60	472	1	470	0

The loan balance after 36 months would be $10,496