5. You are purchasing a car today that costs $25,000. You have been given the following...

5. You are purchasing a car today that costs $25,000. You have been given the following financing options for the car. Option 1 is conventional 4-year financing at an interest rate of 4%, compounded monthly. This option requires monthly payments. Option 2 is a balloon loan which requires monthly payments of $375 for 2 years and then a final balloon payment for the remaining balance. The interest rate on this loan is 2.5%.

a. What is the payment for the conventional loan (option 1)?

b. Prepare an amortization schedule for option 1.

c. What will the balloon payment be for the balloon loan (option 2)?

d. Prepare an amortization schedule for option 2.

e. Which option do you prefer and why? What additional considerations are there with respect to the balloon loan?

Expert Solution

a) The Payment in case of conventional loan = 25000/(1-(1+4%/12)^-48)/(4%/12) = 564.68

b)Following is the amortization table

	Beginning Balance= 25000	PMT =PMT(4%/12,12*4,-25000)	Interest part of PMT=4%/12*Beginning Principal	Principal part of PMT= PMT-Interest	Ending Balance= Beginning balance-Principal part of PMT
1	$25,000.00	$564.48	83.33	$481.14	$24,518.86
2	$24,518.86	$564.48	81.73	$482.75	$24,036.11
3	$24,036.11	$564.48	80.12	$484.36	$23,551.75
4	$23,551.75	$564.48	78.51	$485.97	$23,065.78
5	$23,065.78	$564.48	76.89	$487.59	$22,578.19
6	$22,578.19	$564.48	75.26	$489.22	$22,088.98
7	$22,088.98	$564.48	73.63	$490.85	$21,598.13
8	$21,598.13	$564.48	71.99	$492.48	$21,105.65
9	$21,105.65	$564.48	70.35	$494.12	$20,611.52
10	$20,611.52	$564.48	68.71	$495.77	$20,115.75
11	$20,115.75	$564.48	67.05	$497.42	$19,618.33
12	$19,618.33	$564.48	65.39	$499.08	$19,119.25
13	$19,119.25	$564.48	63.73	$500.75	$18,618.50
14	$18,618.50	$564.48	62.06	$502.41	$18,116.09
15	$18,116.09	$564.48	60.39	$504.09	$17,612.00
16	$17,612.00	$564.48	58.71	$505.77	$17,106.23
17	$17,106.23	$564.48	57.02	$507.46	$16,598.77
18	$16,598.77	$564.48	55.33	$509.15	$16,089.63
19	$16,089.63	$564.48	53.63	$510.84	$15,578.78
20	$15,578.78	$564.48	51.93	$512.55	$15,066.23
21	$15,066.23	$564.48	50.22	$514.26	$14,551.98
22	$14,551.98	$564.48	48.51	$515.97	$14,036.01
23	$14,036.01	$564.48	46.79	$517.69	$13,518.32
24	$13,518.32	$564.48	45.06	$519.42	$12,998.90
25	$12,998.90	$564.48	43.33	$521.15	$12,477.76
26	$12,477.76	$564.48	41.59	$522.88	$11,954.87
27	$11,954.87	$564.48	39.85	$524.63	$11,430.25
28	$11,430.25	$564.48	38.10	$526.38	$10,903.87
29	$10,903.87	$564.48	36.35	$528.13	$10,375.74
30	$10,375.74	$564.48	34.59	$529.89	$9,845.85
31	$9,845.85	$564.48	32.82	$531.66	$9,314.19
32	$9,314.19	$564.48	31.05	$533.43	$8,780.76
33	$8,780.76	$564.48	29.27	$535.21	$8,245.56
34	$8,245.56	$564.48	27.49	$536.99	$7,708.57
35	$7,708.57	$564.48	25.70	$538.78	$7,169.78
36	$7,169.78	$564.48	23.90	$540.58	$6,629.21
37	$6,629.21	$564.48	22.10	$542.38	$6,086.83
38	$6,086.83	$564.48	20.29	$544.19	$5,542.64
39	$5,542.64	$564.48	18.48	$546.00	$4,996.64
40	$4,996.64	$564.48	16.66	$547.82	$4,448.82
41	$4,448.82	$564.48	14.83	$549.65	$3,899.17
42	$3,899.17	$564.48	13.00	$551.48	$3,347.69
43	$3,347.69	$564.48	11.16	$553.32	$2,794.38
44	$2,794.38	$564.48	9.31	$555.16	$2,239.21
45	$2,239.21	$564.48	7.46	$557.01	$1,682.20
46	$1,682.20	$564.48	5.61	$558.87	$1,123.33
47	$1,123.33	$564.48	3.74	$560.73	$562.60
48	$562.60	$564.48	1.88	$562.60	($0.00)

c) Loan amount = 25,000
PV of annuity payment = 375*(1-(1+2.5%)^-24)/2.5% = 8769.80
Balloon Payment /(1+2.5%/12)^24 = 25,000 - 8769.80
Balloon Payment = 17061.45

d)

	Beginning Balance= 25000	PMT =375	Interest part of PMT=2.5%/12*Beginning Principal	Principal part of PMT= PMT-Interest	Ending Balance= Beginning balance-Principal part of PMT
1	$25,000.00	$375.00	52.08	$322.92	$24,677.08
2	$24,677.08	$375.00	51.41	$323.59	$24,353.49
3	$24,353.49	$375.00	50.74	$324.26	$24,029.23
4	$24,029.23	$375.00	50.06	$324.94	$23,704.29
5	$23,704.29	$375.00	49.38	$325.62	$23,378.68
6	$23,378.68	$375.00	48.71	$326.29	$23,052.38
7	$23,052.38	$375.00	48.03	$326.97	$22,725.41
8	$22,725.41	$375.00	47.34	$327.66	$22,397.75
9	$22,397.75	$375.00	46.66	$328.34	$22,069.41
10	$22,069.41	$375.00	45.98	$329.02	$21,740.39
11	$21,740.39	$375.00	45.29	$329.71	$21,410.68
12	$21,410.68	$375.00	44.61	$330.39	$21,080.29
13	$21,080.29	$375.00	43.92	$331.08	$20,749.21
14	$20,749.21	$375.00	43.23	$331.77	$20,417.43
15	$20,417.43	$375.00	42.54	$332.46	$20,084.97
16	$20,084.97	$375.00	41.84	$333.16	$19,751.81
17	$19,751.81	$375.00	41.15	$333.85	$19,417.96
18	$19,417.96	$375.00	40.45	$334.55	$19,083.42
19	$19,083.42	$375.00	39.76	$335.24	$18,748.17
20	$18,748.17	$375.00	39.06	$335.94	$18,412.23
21	$18,412.23	$375.00	38.36	$336.64	$18,075.59
22	$18,075.59	$375.00	37.66	$337.34	$17,738.25
23	$17,738.25	$375.00	36.95	$338.05	$17,400.20
24	$17,400.20	$375.00	36.25	$338.75	$17,061.45

Balloon Payment = 17,061.45
e) I would prefer a balloon payment because interest rate is less by 1.5%
Other factors in balloon payment is the borrower's profile and opportunity loss to the bank for the prepayment of loan.

Please Discuss in case of Doubt

Best of Luck. God Bless
Please Rate Well

jeff jeffy answered 2 years ago

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