Question

You have just bought a car. The $50,000 car loan from the finance company involves monthly payments made at the end of the month, over 60 months. However, at the end of the loan, there is a lump sum payment, called a balloon payment of $30,000.

Assume the interest rate applicable is 6% p.a. monthly rest throughout the loan tenure.

(a) Discuss, using time value concepts of PV or FV of single sums, or multiple sums, etc., how you can compute the first monthly repayment. Show the computations to solve for the monthly repayment amount.           

(b) Explain and compute the interest amount of the first monthly repayment.           

(c) Explain and calculate the interest amount of the 13th monthly repayment.           

(d) Discuss why the finance company offers the balloon scheme instead of the standard loan scheme without a balloon payment.           

Note: You are to provide explanations of the computations you made. Just providing the answer from the financial calculator is not sufficient.

Answer 1

PV = $50000, interest (i) = 6/12 = 0.5%= 0.005 (since the payments are made monthly, the annual interest rate is divided by number of months), number of periods (n) = 60 months (periods)

a. PV= sum of all annuities for 60 months * installment amount (y)+ PV of balloon payment of $30000 made at the end of 60 months

50000 = 51.7255 y + (30000* 0.741372) (refer table below )

50000-22241.166= 51.7255y (discounting is done for Y1 as : 1/(1+i) = 1/(1+0.005)= 1/1.005= 0.995025)

y= 27758.83/51.7255

y=536.565 . So monthly installment is $536.565 (rounded off to 537 in the table below)

Period	PV factor	Loan amount (L)	Interest (Int)	Repayment(R)	Balance (L+Int-R)
1	0.995025	50,000	250	537	49,713
2	0.990075	49,713	249	537	49,425
3	0.985149	49,425	247	537	49,136
4	0.980248	49,136	246	537	48,845
5	0.975371	48,845	244	537	48,552
6	0.970518	48,552	243	537	48,258
7	0.96569	48,258	241	537	47,963
8	0.960885	47,963	240	537	47,666
9	0.956105	47,666	238	537	47,368
10	0.951348	47,368	237	537	47,068
11	0.946615	47,068	235	537	46,767
12	0.941905	46,767	234	537	46,464
13	0.937219	46,464	232	537	46,160
14	0.932556	46,160	231	537	45,854
15	0.927917	45,854	229	537	45,546
16	0.9233	45,546	228	537	45,237
17	0.918707	45,237	226	537	44,927
18	0.914136	44,927	225	537	44,615
19	0.909588	44,615	223	537	44,301
20	0.905063	44,301	222	537	43,986
21	0.90056	43,986	220	537	43,669
22	0.89608	43,669	218	537	43,351
23	0.891622	43,351	217	537	43,031
24	0.887186	43,031	215	537	42,710
25	0.882772	42,710	214	537	42,387
26	0.87838	42,387	212	537	42,062
27	0.87401	42,062	210	537	41,736
28	0.869662	41,736	209	537	41,408
29	0.865335	41,408	207	537	41,078
30	0.86103	41,078	205	537	40,747
31	0.856746	40,747	204	537	40,414
32	0.852484	40,414	202	537	40,079
33	0.848242	40,079	200	537	39,743
34	0.844022	39,743	199	537	39,405
35	0.839823	39,405	197	537	39,065
36	0.835645	39,065	195	537	38,724
37	0.831487	38,724	194	537	38,381
38	0.827351	38,381	192	537	38,036
39	0.823235	38,036	190	537	37,690
40	0.819139	37,690	188	537	37,342
41	0.815064	37,342	187	537	36,992
42	0.811009	36,992	185	537	36,640
43	0.806974	36,640	183	537	36,286
44	0.802959	36,286	181	537	35,931
45	0.798964	35,931	180	537	35,574
46	0.794989	35,574	178	537	35,215
47	0.791034	35,215	176	537	34,855
48	0.787098	34,855	174	537	34,493
49	0.783182	34,493	172	537	34,128
50	0.779286	34,128	171	537	33,762
51	0.775409	33,762	169	537	33,394
52	0.771551	33,394	167	537	33,025
53	0.767713	33,025	165	537	32,653
54	0.763893	32,653	163	537	32,280
55	0.760093	32,280	161	537	31,905
56	0.756311	31,905	160	537	31,527
57	0.752548	31,527	158	537	31,148
58	0.748804	31,148	156	537	30,768
59	0.745079	30,768	154	537	30,385
60	0.741372	30,385	152	537	30,000

b. Loan amount = 50000

Interest in 1st month = Loan * interest rate = 50000 * 0.005 = 250

c. Please refer table above, the 13th repayment will have interest portion of $232 (calculated @ 0.005% on opening balance of $ 46464.

d. if the balloon schemen is offered becasue the major portion of loan amount remains unpaid, which leads to higher interest income for the finance company. Under this scheme, the total interest earned by the finance company is $12199. If the balloon scheme was not offered, the monthly repayments would have been higher , leading to lower interest income.