## 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