Question

You have just purchased a car and taken out a

$ 48 comma 000$48,000

loan. The loan has a five-year term with monthly payments and an APR of

5.8 %5.8%.

a. How much will you pay in interest, and how much will you pay in principal, during the first month, second month, and first year? (Hint: Compute the loan balance after one month, two months, and one year.)

b. How much will you pay in interest, and how much will you pay in principal, during the fourth year (i.e., between three and four years from now)?

(Note: Be careful not to round any intermediate steps less than six decimal places.)

Answer 1

Loan amount	$48,000
time to pay	5yrs
rate of interest	5.80%
PV	$48,000
NPER	60	(5 yrs x 12)
Rate	0.4833%	(5.8%/12)
PMT	$923.52	Loan emi
	=PMT(5.8%/12,60,-48000)
For answering, we will prepare amortization schedule
Period	EMI	Interest	Principal	Loan balance
0				$                                                   48,000.00
1	$923.52	$        232.00	$ 691.52	$                                                   47,308.48
2	$923.52	$        228.66	$ 694.86	$                                                   46,613.62
3	$923.52	$        225.30	$ 698.22	$                                                   45,915.40
4	$923.52	$        221.92	$ 701.60	$                                                   45,213.80
5	$923.52	$        218.53	$ 704.99	$                                                   44,508.81
6	$923.52	$        215.13	$ 708.39	$                                                   43,800.42
7	$923.52	$        211.70	$ 711.82	$                                                   43,088.60
8	$923.52	$        208.26	$ 715.26	$                                                   42,373.34
9	$923.52	$        204.80	$ 718.72	$                                                   41,654.63
10	$923.52	$        201.33	$ 722.19	$                                                   40,932.44
11	$923.52	$        197.84	$ 725.68	$                                                   40,206.76
12	$923.52	$        194.33	$ 729.19	$                                                   39,477.57
13	$923.52	$        190.81	$ 732.71	$                                                   38,744.86
14	$923.52	$        187.27	$ 736.25	$                                                   38,008.61
15	$923.52	$        183.71	$ 739.81	$                                                   37,268.80
16	$923.52	$        180.13	$ 743.39	$                                                   36,525.41
17	$923.52	$        176.54	$ 746.98	$                                                   35,778.43
18	$923.52	$        172.93	$ 750.59	$                                                   35,027.84
19	$923.52	$        169.30	$ 754.22	$                                                   34,273.62
20	$923.52	$        165.66	$ 757.86	$                                                   33,515.75
21	$923.52	$        161.99	$ 761.53	$                                                   32,754.23
22	$923.52	$        158.31	$ 765.21	$                                                   31,989.02
23	$923.52	$        154.61	$ 768.91	$                                                   31,220.11
24	$923.52	$        150.90	$ 772.62	$                                                   30,447.49
25	$923.52	$        147.16	$ 776.36	$                                                   29,671.13
26	$923.52	$        143.41	$ 780.11	$                                                   28,891.02
27	$923.52	$        139.64	$ 783.88	$                                                   28,107.14
28	$923.52	$        135.85	$ 787.67	$                                                   27,319.47
29	$923.52	$        132.04	$ 791.48	$                                                   26,528.00
30	$923.52	$        128.22	$ 795.30	$                                                   25,732.70
31	$923.52	$        124.37	$ 799.15	$                                                   24,933.55
32	$923.52	$        120.51	$ 803.01	$                                                   24,130.54
33	$923.52	$        116.63	$ 806.89	$                                                   23,323.65
34	$923.52	$        112.73	$ 810.79	$                                                   22,512.87
35	$923.52	$        108.81	$ 814.71	$                                                   21,698.16
36	$923.52	$        104.87	$ 818.65	$                                                   20,879.51
37	$923.52	$        100.92	$ 822.60	$                                                   20,056.91
38	$923.52	$          96.94	$ 826.58	$                                                   19,230.33
39	$923.52	$          92.95	$ 830.57	$                                                   18,399.76
40	$923.52	$          88.93	$ 834.59	$                                                   17,565.17
41	$923.52	$          84.90	$ 838.62	$                                                   16,726.55
42	$923.52	$          80.84	$ 842.68	$                                                   15,883.87
43	$923.52	$          76.77	$ 846.75	$                                                   15,037.13
44	$923.52	$          72.68	$ 850.84	$                                                   14,186.28
45	$923.52	$          68.57	$ 854.95	$                                                   13,331.33
46	$923.52	$          64.43	$ 859.09	$                                                   12,472.25
47	$923.52	$          60.28	$ 863.24	$                                                   11,609.01
48	$923.52	$          56.11	$ 867.41	$                                                   10,741.60
49	$923.52	$          51.92	$ 871.60	$                                                     9,870.00
50	$923.52	$          47.70	$ 875.82	$                                                     8,994.18
51	$923.52	$          43.47	$ 880.05	$                                                     8,114.13
52	$923.52	$          39.22	$ 884.30	$                                                     7,229.83
53	$923.52	$          34.94	$ 888.58	$                                                     6,341.26
54	$923.52	$          30.65	$ 892.87	$                                                     5,448.39
55	$923.52	$          26.33	$ 897.19	$                                                     4,551.20
56	$923.52	$          22.00	$ 901.52	$                                                     3,649.68
57	$923.52	$          17.64	$ 905.88	$                                                     2,743.80
58	$923.52	$          13.26	$ 910.26	$                                                     1,833.54
59	$923.52	$            8.86	$ 914.66	$                                                         918.88
60	$923.52	$            4.44	$ 919.08	$                                                           (0.20)
Hint for first row, 923.52 as calculated above
232 = 48000 x 5.8%/12
691.52 = 923.52-232
47308.48 = 48000-691.52
other rows are calculated similarly
	Interest	Principal
1st month	232	691.52	Ans a
2nd month	228.66	694.86
1 year (Sum for 1 -12 month)	2559.81	8522.43
4th Year(Sum for 37-48 months)	944.33	10137.91	Ans b

as an alternative we can also calculate using excel formula
	Interest	Principal		Formula
1st month	($232.00)	($691.52)		=CUMIPMT(5.8%/12,60,48000,1,1,0)	=CUMPRINC(5.8%/12,60,48000,1,1,0)
2nd month	($228.66)	($694.86)		=CUMIPMT(5.8%/12,60,48000,2,2,0)	=CUMPRINC(5.8%/12,60,48000,2,2,0)
1 year (Sum for 1 -12 month)	($2,559.81)	($8,522.39)		=CUMIPMT(5.8%/12,60,48000,1,12,0)	=CUMPRINC(5.8%/12,60,48000,1,12,0)
4th Year(Sum for 37-48 months)	($944.34)	($10,137.87)		=CUMIPMT(5.8%/12,60,48000,37,48,0)	=CUMPRINC(5.8%/12,60,48000,37,48,0)