Question

Anna decides to take out a four-year loan for $30,000 to purchase a new car. Her loan officer tells her that she will make equal, monthly payments for the loan at an interest rate of 8 percent per year.

How much, in total, did Anna pay in interest over the course of the loan?

Answer 1

Total interest paid = 5154.61

Workings

Rate = 8%/12 = 0.67%

Monthly instalment = (30,000*0.67% *(1+0.67%) ^ 48 )/ ((1+0.67%)^48-1)

= 732.39

Loan amortization schedule:

Month	Beginning Balance	Monthly payment	Principal	Interest	Ending balance
			(Monthly payment - Interest)	(Beginning balance*8%/12)	(Beg bal- Principal)
1	30,000	732.38767	532.3876702	200	29,468
2	29,468	732.38767	535.9369214	196.4507489	28,932
3	28,932	732.38767	539.5098342	192.8778361	28,392
4	28,392	732.38767	543.1065664	189.2811038	27,849
5	27,849	732.38767	546.7272769	185.6603934	27,302
6	27,302	732.38767	550.3721254	182.0155449	26,752
7	26,752	732.38767	554.0412729	178.3463974	26,198
8	26,198	732.38767	557.7348814	174.6527889	25,640
9	25,640	732.38767	561.4531139	170.9345563	25,079
10	25,079	732.38767	565.1961347	167.1915356	24,514
11	24,514	732.38767	568.9641089	163.4235614	23,945
12	23,945	732.38767	572.757203	159.6304673	23,372
13	23,372	732.38767	576.5755843	155.8120859	22,795
14	22,795	732.38767	580.4194215	151.9682487	22,215
15	22,215	732.38767	584.2888843	148.0987859	21,631
16	21,631	732.38767	588.1841436	144.2035267	21,042
17	21,042	732.38767	592.1053712	140.282299	20,450
18	20,450	732.38767	596.0527403	136.3349299	19,854
19	19,854	732.38767	600.0264253	132.361245	19,254
20	19,254	732.38767	604.0266014	128.3610688	18,650
21	18,650	732.38767	608.0534455	124.3342248	18,042
22	18,042	732.38767	612.1071351	120.2805352	17,430
23	17,430	732.38767	616.1878493	116.1998209	16,814
24	16,814	732.38767	620.2957683	112.0919019	16,193
25	16,193	732.38767	624.4310734	107.9565968	15,569
26	15,569	732.38767	628.5939473	103.793723	14,940
27	14,940	732.38767	632.7845736	99.60309667	14,308
28	14,308	732.38767	637.0031374	95.38453284	13,671
29	13,671	732.38767	641.249825	91.13784526	13,029
30	13,029	732.38767	645.5248238	86.86284643	12,384
31	12,384	732.38767	649.8283226	82.5593476	11,734
32	11,734	732.38767	654.1605115	78.22715878	11,080
33	11,080	732.38767	658.5215815	73.86608871	10,421
34	10,421	732.38767	662.9117254	69.47594483	9,758
35	9,758	732.38767	667.3311369	65.05653333	9,091
36	9,091	732.38767	671.7800112	60.60765908	8,419
37	8,419	732.38767	676.2585446	56.12912567	7,743
38	7,743	732.38767	680.7669349	51.62073538	7,062
39	7,062	732.38767	685.3053811	47.08228914	6,377
40	6,377	732.38767	689.8740836	42.5135866	5,687
41	5,687	732.38767	694.4732442	37.91442605	4,993
42	4,993	732.38767	699.1030658	33.28460442	4,294
43	4,294	732.38767	703.7637529	28.62391731	3,590
44	3,590	732.38767	708.4555113	23.93215896	2,881
45	2,881	732.38767	713.178548	19.20912222	2,168
46	2,168	732.38767	717.9330717	14.45459856	1,450
47	1,450	732.38767	722.7192922	9.668378086	728
48	728	732.38767	727.5374208	4.850249472	0
Total			30000	5154.61