Question

You have just taken out a $ 30000 car loan with a 6 % ​APR, compounded monthly. The loan is for five years. When you make your first payment in one​ month, how much of the payment will go toward the principal of the loan and how much will go toward​ interest?  ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.)

When you make your first​ payment, ​ $(blank)? will go toward the principal of the loan and ​$ (blank)? will go toward the interest.

Answer 1

EAR = [(1 +stated rate/no. of compounding periods) ^no. of compounding periods - 1]* 100

Effective Annual Rate = ((1+6/12*100)^12-1)*100

Effective Annual Rate% = 6.17

	Monthly rate(M)=	yearly rate/12=	0.51%	Monthly payment=	582.36
Month	Beginning balance (A)	Monthly payment	Interest = M*A	Principal paid	Ending balance
1	30000.00	582.36	154.25 (answer 2)	428.11 (answer 1)	29571.89
2	29571.89	582.36	152.05	430.31	29141.58
3	29141.58	582.36	149.84	432.52	28709.06
4	28709.06	582.36	147.61	434.75	28274.31
5	28274.31	582.36	145.38	436.98	27837.33
6	27837.33	582.36	143.13	439.23	27398.10
7	27398.10	582.36	140.87	441.49	26956.62
8	26956.62	582.36	138.60	443.76	26512.86
9	26512.86	582.36	136.32	446.04	26066.82
10	26066.82	582.36	134.03	448.33	25618.49
11	25618.49	582.36	131.72	450.64	25167.85
12	25167.85	582.36	129.40	452.95	24714.90
13	24714.90	582.36	127.08	455.28	24259.62
14	24259.62	582.36	124.73	457.62	23801.99
15	23801.99	582.36	122.38	459.98	23342.02
16	23342.02	582.36	120.02	462.34	22879.68
17	22879.68	582.36	117.64	464.72	22414.96
18	22414.96	582.36	115.25	467.11	21947.85
19	21947.85	582.36	112.85	469.51	21478.34
20	21478.34	582.36	110.43	471.92	21006.42
21	21006.42	582.36	108.01	474.35	20532.07
22	20532.07	582.36	105.57	476.79	20055.28
23	20055.28	582.36	103.12	479.24	19576.04
24	19576.04	582.36	100.65	481.70	19094.33
25	19094.33	582.36	98.18	484.18	18610.15
26	18610.15	582.36	95.69	486.67	18123.48
27	18123.48	582.36	93.18	489.17	17634.30
28	17634.30	582.36	90.67	491.69	17142.61
29	17142.61	582.36	88.14	494.22	16648.40
30	16648.40	582.36	85.60	496.76	16151.64
31	16151.64	582.36	83.05	499.31	15652.33
32	15652.33	582.36	80.48	501.88	15150.45
33	15150.45	582.36	77.90	504.46	14645.99
34	14645.99	582.36	75.30	507.05	14138.94
35	14138.94	582.36	72.70	509.66	13629.27
36	13629.27	582.36	70.08	512.28	13116.99
37	13116.99	582.36	67.44	514.92	12602.08
38	12602.08	582.36	64.80	517.56	12084.52
39	12084.52	582.36	62.13	520.22	11564.29
40	11564.29	582.36	59.46	522.90	11041.39
41	11041.39	582.36	56.77	525.59	10515.81
42	10515.81	582.36	54.07	528.29	9987.52
43	9987.52	582.36	51.35	531.01	9456.51
44	9456.51	582.36	48.62	533.74	8922.77
45	8922.77	582.36	45.88	536.48	8386.29
46	8386.29	582.36	43.12	539.24	7847.05
47	7847.05	582.36	40.35	542.01	7305.04
48	7305.04	582.36	37.56	544.80	6760.24
49	6760.24	582.36	34.76	547.60	6212.64
50	6212.64	582.36	31.94	550.42	5662.23
51	5662.23	582.36	29.11	553.25	5108.98
52	5108.98	582.36	26.27	556.09	4552.89
53	4552.89	582.36	23.41	558.95	3993.95
54	3993.95	582.36	20.54	561.82	3432.12
55	3432.12	582.36	17.65	564.71	2867.41
56	2867.41	582.36	14.74	567.62	2299.80
57	2299.80	582.36	11.82	570.53	1729.26
58	1729.26	582.36	8.89	573.47	1155.80
59	1155.80	582.36	5.94	576.42	579.38
60	579.38	582.36	2.98	579.38	0.00

Where

Interest paid = Beginning balance * Monthly interest rate

Principal = Monthly payment – interest paid

Ending balance = beginning balance – principal paid

Beginning balance = previous Month ending balance