Question

Your firm has taken out a $ 455, 000 loan with 8.6 % APR​ (compounded monthly) for some commercial property. As is common in commercial real​ estate, the loan is a 5​-year loan based on a 15​-year amortization. This means that your loan payments will be calculated as if you will take 15 years to pay off the​ loan, but you actually must do so in 5 years. To do​ this, you will make 59 equal payments based on the 15​-year amortization schedule and then make a final 60th payment to pay the remaining balance.  ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.)

a. What will your monthly payments​ be?

b. What will your final payment​ be?

Answer 1

a) PV of loan = 455,000
Rate per month = 8.6%/12
Number of Periods = 15*12 = 180
Monthly Payments = 455,000*(1-(1+8.6%/12)^-180)/(8.6%/12) = 4507.28

b) For final payments using amortization table for 5*12 = 60 months

	Beginning Balance= 455,000	PMT =PMT(8.6%/12,180,-455000)	Interest part of PMT=8.6%/12*Beginning Principal	Principal part of PMT= PMT-Interest	Ending Balance= Beginning balance-Principal part of PMT
1	$455,000.00	$4,507.28	3260.83	$1,246.44	$453,753.56
2	$453,753.56	$4,507.28	3251.90	$1,255.38	$452,498.18
3	$452,498.18	$4,507.28	3242.90	$1,264.37	$451,233.81
4	$451,233.81	$4,507.28	3233.84	$1,273.43	$449,960.38
5	$449,960.38	$4,507.28	3224.72	$1,282.56	$448,677.82
6	$448,677.82	$4,507.28	3215.52	$1,291.75	$447,386.07
7	$447,386.07	$4,507.28	3206.27	$1,301.01	$446,085.06
8	$446,085.06	$4,507.28	3196.94	$1,310.33	$444,774.72
9	$444,774.72	$4,507.28	3187.55	$1,319.72	$443,455.00
10	$443,455.00	$4,507.28	3178.09	$1,329.18	$442,125.82
11	$442,125.82	$4,507.28	3168.57	$1,338.71	$440,787.11
12	$440,787.11	$4,507.28	3158.97	$1,348.30	$439,438.81
13	$439,438.81	$4,507.28	3149.31	$1,357.96	$438,080.84
14	$438,080.84	$4,507.28	3139.58	$1,367.70	$436,713.15
15	$436,713.15	$4,507.28	3129.78	$1,377.50	$435,335.65
16	$435,335.65	$4,507.28	3119.91	$1,387.37	$433,948.28
17	$433,948.28	$4,507.28	3109.96	$1,397.31	$432,550.97
18	$432,550.97	$4,507.28	3099.95	$1,407.33	$431,143.64
19	$431,143.64	$4,507.28	3089.86	$1,417.41	$429,726.23
20	$429,726.23	$4,507.28	3079.70	$1,427.57	$428,298.66
21	$428,298.66	$4,507.28	3069.47	$1,437.80	$426,860.85
22	$426,860.85	$4,507.28	3059.17	$1,448.11	$425,412.75
23	$425,412.75	$4,507.28	3048.79	$1,458.48	$423,954.26
24	$423,954.26	$4,507.28	3038.34	$1,468.94	$422,485.33
25	$422,485.33	$4,507.28	3027.81	$1,479.46	$421,005.86
26	$421,005.86	$4,507.28	3017.21	$1,490.07	$419,515.79
27	$419,515.79	$4,507.28	3006.53	$1,500.75	$418,015.05
28	$418,015.05	$4,507.28	2995.77	$1,511.50	$416,503.55
29	$416,503.55	$4,507.28	2984.94	$1,522.33	$414,981.21
30	$414,981.21	$4,507.28	2974.03	$1,533.24	$413,447.97
31	$413,447.97	$4,507.28	2963.04	$1,544.23	$411,903.74
32	$411,903.74	$4,507.28	2951.98	$1,555.30	$410,348.44
33	$410,348.44	$4,507.28	2940.83	$1,566.45	$408,781.99
34	$408,781.99	$4,507.28	2929.60	$1,577.67	$407,204.32
35	$407,204.32	$4,507.28	2918.30	$1,588.98	$405,615.34
36	$405,615.34	$4,507.28	2906.91	$1,600.37	$404,014.98
37	$404,014.98	$4,507.28	2895.44	$1,611.84	$402,403.14
38	$402,403.14	$4,507.28	2883.89	$1,623.39	$400,779.76
39	$400,779.76	$4,507.28	2872.25	$1,635.02	$399,144.73
40	$399,144.73	$4,507.28	2860.54	$1,646.74	$397,498.00
41	$397,498.00	$4,507.28	2848.74	$1,658.54	$395,839.46
42	$395,839.46	$4,507.28	2836.85	$1,670.43	$394,169.03
43	$394,169.03	$4,507.28	2824.88	$1,682.40	$392,486.63
44	$392,486.63	$4,507.28	2812.82	$1,694.45	$390,792.18
45	$390,792.18	$4,507.28	2800.68	$1,706.60	$389,085.58
46	$389,085.58	$4,507.28	2788.45	$1,718.83	$387,366.75
47	$387,366.75	$4,507.28	2776.13	$1,731.15	$385,635.60
48	$385,635.60	$4,507.28	2763.72	$1,743.55	$383,892.05
49	$383,892.05	$4,507.28	2751.23	$1,756.05	$382,136.00
50	$382,136.00	$4,507.28	2738.64	$1,768.63	$380,367.36
51	$380,367.36	$4,507.28	2725.97	$1,781.31	$378,586.05
52	$378,586.05	$4,507.28	2713.20	$1,794.08	$376,791.98
53	$376,791.98	$4,507.28	2700.34	$1,806.93	$374,985.05
54	$374,985.05	$4,507.28	2687.39	$1,819.88	$373,165.16
55	$373,165.16	$4,507.28	2674.35	$1,832.93	$371,332.24
56	$371,332.24	$4,507.28	2661.21	$1,846.06	$369,486.18
57	$369,486.18	$4,507.28	2647.98	$1,859.29	$367,626.88
58	$367,626.88	$4,507.28	2634.66	$1,872.62	$365,754.27
59	$365,754.27	$4,507.28	2621.24	$1,886.04	$363,868.23
60	$363,868.23	$4,507.28	2607.72	$1,899.55	$361,968.68

Final Payment is the ending principal after 60 months = 361,968.68

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