Question

Below is a common problem in which the payments are not the same time period as the interest rate or the time period. In order to compute the payment correctly you need to adjust all variables so that they are the same period as the payment (note some calculators might do this automatically, you can set them so they do not do automatically make this correction).

So if the problem has monthly payments, but the problem has an annual interest rate and time period over years, you would need to divide the interest by 12 and multiply the time period by 12.

You would make similar adjustments if the payment was per day or semi annual.

You are considering buying a new motorcycle.  You are going to borrow $10,370.  If you can negotiate a nominal annual interest rate of 6 percent (i.e. 6% equals the APR) and you wish to pay for the car over a 3-year period, what are your monthly car payments?

Answer 1

	Monthly rate(M)=	yearly rate/12=	0.50%	Monthly payment=	315.48
Month	Beginning balance (A)	Monthly payment	Interest = M*A	Principal paid	Ending balance
1	10370.00	315.48	51.85	263.63	10106.37
2	10106.37	315.48	50.53	264.94	9841.43
3	9841.43	315.48	49.21	266.27	9575.16
4	9575.16	315.48	47.88	267.60	9307.56
5	9307.56	315.48	46.54	268.94	9038.63
6	9038.63	315.48	45.19	270.28	8768.34
7	8768.34	315.48	43.84	271.63	8496.71
8	8496.71	315.48	42.48	272.99	8223.72
9	8223.72	315.48	41.12	274.36	7949.36
10	7949.36	315.48	39.75	275.73	7673.63
11	7673.63	315.48	38.37	277.11	7396.52
12	7396.52	315.48	36.98	278.49	7118.03
13	7118.03	315.48	35.59	279.89	6838.15
14	6838.15	315.48	34.19	281.28	6556.86
15	6556.86	315.48	32.78	282.69	6274.17
16	6274.17	315.48	31.37	284.10	5990.07
17	5990.07	315.48	29.95	285.53	5704.54
18	5704.54	315.48	28.52	286.95	5417.59
19	5417.59	315.48	27.09	288.39	5129.20
20	5129.20	315.48	25.65	289.83	4839.37
21	4839.37	315.48	24.20	291.28	4548.09
22	4548.09	315.48	22.74	292.74	4255.36
23	4255.36	315.48	21.28	294.20	3961.16
24	3961.16	315.48	19.81	295.67	3665.49
25	3665.49	315.48	18.33	297.15	3368.34
26	3368.34	315.48	16.84	298.63	3069.71
27	3069.71	315.48	15.35	300.13	2769.58
28	2769.58	315.48	13.85	301.63	2467.95
29	2467.95	315.48	12.34	303.14	2164.82
30	2164.82	315.48	10.82	304.65	1860.16
31	1860.16	315.48	9.30	306.17	1553.99
32	1553.99	315.48	7.77	307.71	1246.28
33	1246.28	315.48	6.23	309.24	937.04
34	937.04	315.48	4.69	310.79	626.25
35	626.25	315.48	3.13	312.34	313.91
36	313.91	315.48	1.57	313.91	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