Question

ou want to buy a car, and a local bank will lend you $10,000. The loan would be fully amortized over 5 years (60 months), and the nominal interest rate would be 15%, with interest paid monthly. What is the monthly loan payment? Do not round intermediate calculations. Round your answer to the nearest cent.

$  

What is the loan's EFF%? Do not round intermediate calculations. Round your answer to two decimal places.

%

Answer 1

monthly loan repayment= P*R*(1+R)^N]/[(1+R)^N-1

where, P= Principal= $10,000, R= monthly rate of interest=1.25% (15%/12), N= number of payments= 60 (5*12 months)

monthly loan payment=$10,000*0.0125*(1+0.0125)^60/[(1+0.0125)^60]-1 Monthly repayment is $237.8993 or $238

Monthly interest payment= R/N*P = (0.15/12)* balance principal outstanding at the beginning of the year

where, P= Principal at the start of the year, R= rate of interest, N= number of payments i.e 12 times in a year

Effective annual interest rate = (1 + (nominal rate / number of compounding periods)) ^ (number of compounding periods) - 1

where, nominal rate= 15%, number of compounding period= 12 i.e 12 months

effective interest rate= (1+(0.15/12))^12-1

effective interest rate= 16.0755%

Below have attached the repayment schedule for your reference.

Month	Starting balance	Repayment	Interest paid	Principal paid	New balance
1	$10,000	237.899	$125	$113	$9,887
2	$9,887	237.899	$124	$114	$9,773
3	$9,773	237.899	$122	$116	$9,657
4	$9,657	237.899	$121	$117	$9,540
5	$9,540	237.899	$119	$119	$9,421
6	$9,421	237.899	$118	$120	$9,301
7	$9,301	237.899	$116	$122	$9,179
8	$9,179	237.899	$115	$123	$9,056
9	$9,056	237.899	$113	$125	$8,932
10	$8,932	237.899	$112	$126	$8,805
11	$8,805	237.899	$110	$128	$8,678
12	$8,678	237.899	$108	$129	$8,548
13	$8,548	237.899	$107	$131	$8,417
14	$8,417	237.899	$105	$133	$8,284
15	$8,284	237.899	$104	$134	$8,150
16	$8,150	237.899	$102	$136	$8,014
17	$8,014	237.899	$100	$138	$7,876
18	$7,876	237.899	$98	$139	$7,737
19	$7,737	237.899	$97	$141	$7,596
20	$7,596	237.899	$95	$143	$7,453
21	$7,453	237.899	$93	$145	$7,308
22	$7,308	237.899	$91	$147	$7,161
23	$7,161	237.899	$90	$148	$7,013
24	$7,013	237.899	$88	$150	$6,863
25	$6,863	237.899	$86	$152	$6,711
26	$6,711	237.899	$84	$154	$6,557
27	$6,557	237.899	$82	$156	$6,401
28	$6,401	237.899	$80	$158	$6,243
29	$6,243	237.899	$78	$160	$6,083
30	$6,083	237.899	$76	$162	$5,921
31	$5,921	237.899	$74	$164	$5,757
32	$5,757	237.899	$72	$166	$5,591
33	$5,591	237.899	$70	$168	$5,423
34	$5,423	237.899	$68	$170	$5,253
35	$5,253	237.899	$66	$172	$5,081
36	$5,081	237.899	$64	$174	$4,906
37	$4,906	237.899	$61	$177	$4,730
38	$4,730	237.899	$59	$179	$4,551
39	$4,551	237.899	$57	$181	$4,370
40	$4,370	237.899	$55	$183	$4,187
41	$4,187	237.899	$52	$186	$4,001
42	$4,001	237.899	$50	$188	$3,813
43	$3,813	237.899	$48	$190	$3,623
44	$3,623	237.899	$45	$193	$3,431
45	$3,431	237.899	$43	$195	$3,236
46	$3,236	237.899	$40	$197	$3,038
47	$3,038	237.899	$38	$200	$2,838
48	$2,838	237.899	$35	$202	$2,636
49	$2,636	237.899	$33	$205	$2,431
50	$2,431	237.899	$30	$208	$2,223
51	$2,223	237.899	$28	$210	$2,013
52	$2,013	237.899	$25	$213	$1,800
53	$1,800	237.899	$23	$215	$1,585
54	$1,585	237.899	$20	$218	$1,367
55	$1,367	237.899	$17	$221	$1,146
56	$1,146	237.899	$14	$224	$923
57	$923	237.899	$12	$226	$696
58	$696	237.899	$9	$229	$467
59	$467	237.899	$6	$232	$235
60	$235	237.899	$3	$235	($0)