Can’t decide between 15 vs 30 year mortgage? Lets’s look at what math says

There are several decisions to be made while buying a house and probably one of the most debatable one is the mortgage term [15 year vs 30 years]. When I asked around, there were folks in both the camps – everyone had a valid point. Quick search shows millions of results about endless discussion that are out there.

What if there was a way to get the flexibility of 30 year mortgage and payment terms (almost) of 15 year? With following assumptions, let’s do some maths to find out:

• Loan amount: 300K
• 30 year interest rate: 4%
• 15 year interest rate: 3%
 30 yr rate 4% Monthly payment \$1,432 Total Cost \$515,609 15 yr rate 3% Monthly payment \$2,072 Total Cost \$372,914

Above table shows the monthly payment and total cost of both the options (use any mortgage calculator online to get the numbers for your loan value). Since most of the loans do not have prepayment penalty meaning you can always pay more than the required monthly payment and the extra goes towards the principal.

Accelerated payment calculation:

If you pay the difference (2072 – 1432 = 640) towards the principal, the total accelerated payment would be \$410,289 which gives you savings of \$105,318 and shortens the time of repayment by 13 years 6 months. But the original saving with the term and interest difference was \$142,695   (\$515,609 – \$372,914) so the accelerated payment method costs you \$37,375 more, which I call the cost of flexibility and piece of mind knowing that if something happens within those years and you can’t afford the higher payment, you’re not stuck with it!

Net Present Value (NPV) of the total payment:

Since the mortgage payment amount is fixed, above calculation wouldn’t be complete without considering the effect of inflation. Let’s consider the NPV of the total payments considering standard 3% inflation:

• 30 year payment NPV: \$340,504
• 15 year payment NPV: \$300,787

Since the payments are in future dollars, the buying power (value) of the dollar will be less compared to the value of dollar today. To put this in perspective, consider what \$100 gets today vs what it bought 20 years ago.

Note: Above calculations doesn’t consider either other payments such as tax, insurance etc. or the tax tax advantages we get from the interest payment.

Opportunity Cost

Opportunity cost should also be considered to look at the bigger picture. Let’s say you take 30 year mortgage and invest the monthly payment difference in stocks, which historically has given 7% return.

total value of investing \$640 every month for 15 years considering 7% annual return is: approx 200,000; which is more than the difference in savings you get from 15 year term.

Paying every 2 weeks:

Lot of online discussions revolve about paying the loan every 2 weeks instead of monthly, with the logic that the interest is based off of the total outstanding principal and if you pay every 2 weeks (half the amount), it lowers the principal and in turn lowers the interest amount in the long run. Check your financing documents to see whether your lender accepts “Partial Payments”; if they don’t, then the amount you pay every 2 weeks will sit in their bank account without being applied towards the loan – which is similar to you giving the bank free loan for 2 weeks.

To sum it up:

While it’s prudent to get 30 year mortgage and invest the difference somewhere else (mortgage is considered good debt), however, there is always an option to pay more and thus early payoff on 30 year terms, which gives flexibility to folks who would like to pay if off sooner.