Question

A mortgage company offers to lend you $85,000; the loan calls for payments of $8,383.86 at the end of each year for 30 years. What interest rate is the mortgage company charging you? Round your answer to two decimal places.

_______%

While Mary Corens was a student at the University of Tennessee, she borrowed $12,000 in student loans at an annual interest rate of 9.20%. If Mary repays $1,500 per year, how long (rounded up to the nearest year) will it take her to repay the loan?

_______year(s)

Answer 1

1.

	Annual rate(M)=	yearly rate/12=	9.15%	Annual payment=	8383.86
Year	Beginning balance (A)	Annual payment	Interest = M*A	Principal paid	Ending balance
1	85000.00	8383.86	7777.50	606.36	84393.64
2	84393.64	8383.86	7722.02	661.84	83731.79
3	83731.79	8383.86	7661.46	722.40	83009.39
4	83009.39	8383.86	7595.36	788.50	82220.89
5	82220.89	8383.86	7523.21	860.65	81360.24
6	81360.24	8383.86	7444.46	939.40	80420.84
7	80420.84	8383.86	7358.50	1025.36	79395.48
8	79395.48	8383.86	7264.68	1119.18	78276.30
9	78276.30	8383.86	7162.28	1221.58	77054.72
10	77054.72	8383.86	7050.51	1333.35	75721.37
11	75721.37	8383.86	6928.50	1455.36	74266.01
12	74266.01	8383.86	6795.34	1588.52	72677.49
13	72677.49	8383.86	6649.99	1733.87	70943.62
14	70943.62	8383.86	6491.34	1892.52	69051.10
15	69051.10	8383.86	6318.17	2065.69	66985.41
16	66985.41	8383.86	6129.16	2254.70	64730.72
17	64730.72	8383.86	5922.86	2461.00	62269.72
18	62269.72	8383.86	5697.68	2686.18	59583.53
19	59583.53	8383.86	5451.89	2931.97	56651.57
20	56651.57	8383.86	5183.62	3200.24	53451.32
21	53451.32	8383.86	4890.79	3493.07	49958.26
22	49958.26	8383.86	4571.18	3812.68	46145.58
23	46145.58	8383.86	4222.32	4161.54	41984.03
24	41984.03	8383.86	3841.54	4542.32	37441.71
25	37441.71	8383.86	3425.92	4957.94	32483.77
26	32483.77	8383.86	2972.26	5411.60	27072.17
27	27072.17	8383.86	2477.10	5906.76	21165.42
28	21165.42	8383.86	1936.63	6447.23	14718.19
29	14718.19	8383.86	1346.71	7037.15	7681.04
30	7681.04	8383.86	702.82	7681.04	0.00

Annual rate %=9.15

Where

Interest paid = Beginning balance * Annual interest rate

Principal = Annual payment – interest paid

Ending balance = beginning balance – principal paid

Beginning balance = previous Year ending balance

2.

	Annual rate(M)=	yearly rate/12=	9.20%	Annual payment=	1500.00
Year	Beginning balance (A)	Annual payment	Interest = M*A	Principal paid	Ending balance
1	12000.00	1500.00	1104.00	396.00	11604.00
2	11604.00	1500.00	1067.57	432.43	11171.57
3	11171.57	1500.00	1027.78	472.22	10699.35
4	10699.35	1500.00	984.34	515.66	10183.69
5	10183.69	1500.00	936.90	563.10	9620.59
6	9620.59	1500.00	885.09	614.91	9005.69
7	9005.69	1500.00	828.52	671.48	8334.21
8	8334.21	1500.00	766.75	733.25	7600.96
9	7600.96	1500.00	699.29	800.71	6800.25
10	6800.25	1500.00	625.62	874.38	5925.87
11	5925.87	1500.00	545.18	954.82	4971.05
12	4971.05	1500.00	457.34	1042.66	3928.38
13	3928.38	1500.00	361.41	1138.59	2789.80
14	2789.80	1500.00	256.66	1243.34	1546.46
15	1546.46	1500.00	142.27	1357.73	188.73
16	188.73	1500.00	17.36	1482.64	-1293.91

Where

Interest paid = Beginning balance * Annual interest rate

Principal = Annual payment – interest paid

Ending balance = beginning balance – principal paid

Beginning balance = previous Year ending balance

N = 15 years