Question

1. A newly divorced father of two, looking to improve his image wants to purchase a Mercedes-Benz in order to impress his young and foxy girlfriend. The car costs $17,999 and the car yard is willing to offer financing. The terms of the deal include a $2000 deposit (which the client has) with the remainder of the balance being repaid in equal monthly installments over the next three years. The car dealer charges 1.25 percent interest rate per month on the balance of the outstanding loan.

Required: Calculate the size of each monthly payment and then prepare a loan amortization schedule to show that as time passes the amount paid in interest by your client is reduced.

Answer 1

Here amount to be financed = 17,999 - 2,000 = $15,999

Nper = 3*12 = 36, rate = 1.25%.

The size of each monthly payment = PMT (1.25%, 36, 15999). This gives a value of $554.61

It can also be computed manually using the formula: P*r*(1+r)^n/(1+r)^n - 1

= 15,999*0.0125*1.0125^36/1.0125^36 - 1

= 312.7692/0.5639

= $554.61

Thus size of each monthly payment = $554.61

Loan amortization schedule:

Month	Loan amount at start of month	Payment	Interest	Principal	Loan amount at end of month
1	15999	554.61	199.99	354.62	15,644.38
2	15,644.38	554.61	195.55	359.06	15,285.32
3	15,285.32	554.61	191.07	363.54	14,921.78
4	14,921.78	554.61	186.52	368.09	14,553.69
5	14,553.69	554.61	181.92	372.69	14,181.00
6	14,181.00	554.61	177.26	377.35	13,803.65
7	13,803.65	554.61	172.55	382.06	13,421.59
8	13,421.59	554.61	167.77	386.84	13,034.75
9	13,034.75	554.61	162.93	391.68	12,643.07
10	12,643.07	554.61	158.04	396.57	12,246.50
11	12,246.50	554.61	153.08	401.53	11,844.97
12	11,844.97	554.61	148.06	406.55	11,438.42
13	11,438.42	554.61	142.98	411.63	11,026.79
14	11,026.79	554.61	137.83	416.78	10,610.01
15	10,610.01	554.61	132.63	421.99	10,188.03
16	10,188.03	554.61	127.35	427.26	9,760.77
17	9,760.77	554.61	122.01	432.60	9,328.17
18	9,328.17	554.61	116.60	438.01	8,890.16
19	8,890.16	554.61	111.13	443.48	8,446.67
20	8,446.67	554.61	105.58	449.03	7,997.65
21	7,997.65	554.61	99.97	454.64	7,543.01
22	7,543.01	554.61	94.29	460.32	7,082.68
23	7,082.68	554.61	88.53	466.08	6,616.61
24	6,616.61	554.61	82.71	471.90	6,144.70
25	6,144.70	554.61	76.81	477.80	5,666.90
26	5,666.90	554.61	70.84	483.77	5,183.13
27	5,183.13	554.61	64.79	489.82	4,693.31
28	4,693.31	554.61	58.67	495.94	4,197.36
29	4,197.36	554.61	52.47	502.14	3,695.22
30	3,695.22	554.61	46.19	508.42	3,186.80
31	3,186.80	554.61	39.83	514.78	2,672.02
32	2,672.02	554.61	33.40	521.21	2,150.81
33	2,150.81	554.61	26.89	527.73	1,623.09
34	1,623.09	554.61	20.29	534.32	1,088.76
35	1,088.76	554.61	13.61	541.00	547.76
36	547.76	554.61	6.85	547.76	0