Tuesday, March 18, 2014

Some thoughts on long term mortgages

Relatively few mortgages have an initial term exceeding 30 years.  Moreover, this proportion is likely to fall because of a recent CFPB rule preventing mortgages with a term of greater than 30 years from being “qualified” mortgages.    Still long-term mortgages are interesting and may play some role in certain real estate projects. 


Questions:

 Show how an increase in the length of the mortgage impacts monthly mortgage payments at different level of interest rates?

How do monthly payments on long-term mortgage differ from monthly payments on interest-only mortgages? 



Analysis:

A table at the bottom of this post has mortgage payments for mortgages with maturities ranging from 15 years to 30 years.   Payment estimates are presented for five levels of interest rates 0%, 3%, 6.0%, 9.0%, and 12.0%.

Calculations were made with the Excel PMT formula.  The mortgage balance is $300,000 and all payments are made at the end of the month.

Observations:

  • The impact of an increase in the mortgage term on mortgage payments has a much larger impact at shorter mortgage terms than at larger mortgage terms.  Consider mortgage contracts with a 6% interest rate.   An increase in the mortgage term from 15 to 20 years reduces payments from $2,532 to  $2,149.  An increase in the mortgage term from 50 to 55 years reduces mortgage payments from $1,579 to $1,558.


  • The payment on a mortgage for a long-term mortgage at high interest rates is identical to payments on interest-only mortgages.  The monthly interest-only payment on a $300,000 mortgage with a 12% interest rate is 0.01*$300,000 or $3,000.  Observe that for mortgage terms of 74 years or longer the actual payment on the 12% interest rate mortgage is $3,000.


  • If the payment on a long-term mortgage at a high interest rate is identical to the payment on an interest-only loan then the case can be made that for long term mortgages at high interest rates there is NO equity build-up at all.






Mortgage Payments by Annual Contract Interest Rate and Mortgage Term
Mortgage Term In Years
Annual Contract Interest Rate
0
0.03
0.06
0.09
0.12
15
-$1,667
-$2,072
-$2,532
-$3,043
-$3,601
16
-$1,563
-$1,969
-$2,434
-$2,954
-$3,521
17
-$1,471
-$1,879
-$2,349
-$2,876
-$3,454
18
-$1,389
-$1,799
-$2,274
-$2,809
-$3,396
19
-$1,316
-$1,728
-$2,208
-$2,751
-$3,346
20
-$1,250
-$1,664
-$2,149
-$2,699
-$3,303
21
-$1,190
-$1,606
-$2,097
-$2,654
-$3,266
22
-$1,136
-$1,554
-$2,049
-$2,614
-$3,234
23
-$1,087
-$1,506
-$2,007
-$2,578
-$3,206
24
-$1,042
-$1,463
-$1,968
-$2,546
-$3,181
25
-$1,000
-$1,423
-$1,933
-$2,518
-$3,160
26
-$962
-$1,386
-$1,901
-$2,492
-$3,141
27
-$926
-$1,352
-$1,872
-$2,469
-$3,124
28
-$893
-$1,321
-$1,845
-$2,449
-$3,110
29
-$862
-$1,292
-$1,821
-$2,430
-$3,097
30
-$833
-$1,265
-$1,799
-$2,414
-$3,086
31
-$806
-$1,240
-$1,778
-$2,399
-$3,076
32
-$781
-$1,216
-$1,759
-$2,385
-$3,067
33
-$758
-$1,194
-$1,742
-$2,373
-$3,059
34
-$735
-$1,174
-$1,726
-$2,362
-$3,053
35
-$714
-$1,155
-$1,711
-$2,352
-$3,047
36
-$694
-$1,136
-$1,697
-$2,343
-$3,041
37
-$676
-$1,119
-$1,684
-$2,335
-$3,037
38
-$658
-$1,103
-$1,672
-$2,327
-$3,032
39
-$641
-$1,088
-$1,661
-$2,320
-$3,029
40
-$625
-$1,074
-$1,651
-$2,314
-$3,025
41
-$610
-$1,060
-$1,641
-$2,308
-$3,023
42
-$595
-$1,048
-$1,632
-$2,303
-$3,020
43
-$581
-$1,036
-$1,624
-$2,299
-$3,018
44
-$568
-$1,024
-$1,616
-$2,294
-$3,016
45
-$556
-$1,013
-$1,609
-$2,291
-$3,014
46
-$543
-$1,003
-$1,602
-$2,287
-$3,012
47
-$532
-$993
-$1,596
-$2,284
-$3,011
48
-$521
-$983
-$1,590
-$2,281
-$3,010
49
-$510
-$974
-$1,584
-$2,278
-$3,009
50
-$500
-$966
-$1,579
-$2,276
-$3,008
51
-$490
-$958
-$1,574
-$2,273
-$3,007
52
-$481
-$950
-$1,570
-$2,271
-$3,006
53
-$472
-$943
-$1,566
-$2,270
-$3,005
54
-$463
-$936
-$1,562
-$2,268
-$3,005
55
-$455
-$929
-$1,558
-$2,266
-$3,004
56
-$446
-$922
-$1,554
-$2,265
-$3,004
57
-$439
-$916
-$1,551
-$2,264
-$3,003
58
-$431
-$910
-$1,548
-$2,262
-$3,003
59
-$424
-$904
-$1,545
-$2,261
-$3,003
60
-$417
-$899
-$1,543
-$2,260
-$3,002
61
-$410
-$894
-$1,540
-$2,260
-$3,002
62
-$403
-$889
-$1,538
-$2,259
-$3,002
63
-$397
-$884
-$1,535
-$2,258
-$3,002
64
-$391
-$879
-$1,533
-$2,257
-$3,001
65
-$385
-$875
-$1,531
-$2,257
-$3,001
66
-$379
-$870
-$1,529
-$2,256
-$3,001
67
-$373
-$866
-$1,528
-$2,256
-$3,001
68
-$368
-$862
-$1,526
-$2,255
-$3,001
69
-$362
-$859
-$1,525
-$2,255
-$3,001
70
-$357
-$855
-$1,523
-$2,254
-$3,001
71
-$352
-$851
-$1,522
-$2,254
-$3,001
72
-$347
-$848
-$1,520
-$2,254
-$3,001
73
-$342
-$845
-$1,519
-$2,253
-$3,000
74
-$338
-$842
-$1,518
-$2,253
-$3,000
75
-$333
-$839
-$1,517
-$2,253
-$3,000
76
-$329
-$836
-$1,516
-$2,252
-$3,000
77
-$325
-$833
-$1,515
-$2,252
-$3,000
78
-$321
-$830
-$1,514
-$2,252
-$3,000
79
-$316
-$828
-$1,513
-$2,252
-$3,000
80
-$313
-$825
-$1,513
-$2,252
-$3,000
81
-$309
-$823
-$1,512
-$2,252
-$3,000
82
-$305
-$820
-$1,511
-$2,251
-$3,000
83
-$301
-$818
-$1,511
-$2,251
-$3,000
84
-$298
-$816
-$1,510
-$2,251
-$3,000
85
-$294
-$814
-$1,509
-$2,251
-$3,000
86
-$291
-$812
-$1,509
-$2,251
-$3,000
87
-$287
-$810
-$1,508
-$2,251
-$3,000
88
-$284
-$808
-$1,508
-$2,251
-$3,000
89
-$281
-$806
-$1,507
-$2,251
-$3,000
90
-$278
-$804
-$1,507
-$2,251
-$3,000
91
-$275
-$803
-$1,506
-$2,251
-$3,000
92
-$272
-$801
-$1,506
-$2,251
-$3,000
93
-$269
-$799
-$1,506
-$2,251
-$3,000
94
-$266
-$798
-$1,505
-$2,250
-$3,000
95
-$263
-$796
-$1,505
-$2,250
-$3,000
96
-$260
-$795
-$1,505
-$2,250
-$3,000
97
-$258
-$793
-$1,505
-$2,250
-$3,000
98
-$255
-$792
-$1,504
-$2,250
-$3,000
99
-$253
-$791
-$1,504
-$2,250
-$3,000
100
-$250
-$789
-$1,504
-$2,250
-$3,000


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