Few borrowers seek a 15-year mortgage when they're buying a home. In February 2015, according to the Mortgage Bankers Association, only 5% of home buyers and 20% of refinancers applied for a 15-year mortgage, and these numbers have been falling in recent years. But if borrowers are put off by the relatively high monthly payment, they are forgoing the chance to save a lot of money, in both senses of the word.

A 15-year mortgage costs much less than to borrow money over 30 years.

• Because the cost of a mortgage is calculated as an annual interest rate, and you are borrowing the money for half as long, you will much less to borrow money for 15 years – usually less than half of what you'd pay over 30 years. The higher the interest rate, the greater the gap between the two mortgages. At 4%, you will pay only about 46% of the interest you pay over the longer loan.

• Because shorter-term loans are less risky and cheaper for banks to fund, a 15-year mortgage typically comes with a lower interest rate – anywhere between a quarter point and whole point less than for a 30-year mortgage.

• If your mortgage is purchased by one of the government-sponsored companies, like Fannie Mae, you will likely end up paying less in fees for a 15-year loan. Fannie Mae and the other government-backed enterprises charge what they call loan level price adjustments that often apply only to, or are higher for, 30-year-mortgages. These fees typically apply to borrowers with lower credit scores, smaller down payments or both. The Federal Housing Administration charges lower mortgage insurance premiums to 15-year borrowers. Most borrowers ultimately pay these costs as part of a higher interest rate, rather than as upfront fees.

• Because the monthly payment is higher, financial planners consider the 15-year-mortgage a form of forced savings – instead of investing those savings in a money market account or stock market equities, you're investing them in your house, which over the long run is also likely to appreciate in value.

Shorter mortgages have higher monthly payments than longer-term loans. For example, a 15-year loan for $300,000 at 4% interest has a monthly payment of $2,219, or 55% higher than a 30-year mortgage for the same amount at the same rate.

• The higher payment might limit the buyer to a more modest house than they would be able to buy with a 30-year loan. (The same monthly payment on a 30-year loan would repay a larger loan.)

• The higher payment requires higher cash reserves – as much as one year's worth of income in liquid savings.

• The higher payment means a borrower may forgo the opportunity to build up other savings, or save for other goals that have incentives, like college tuition or in a 401(k) retirement account, which is both tax-deferred and has an employer contribution. A savvy and disciplined investor would lose the opportunity to invest the difference between the 15-year and 30-year payments in higher-yielding securities.

A 15-year mortgage can save you a lot of money. Imagine a $300,000 loan, available at 3.25% for 15 years or at 4% for 30 years. The combined effect of the faster amortization and the lower interest rate means that borrowing the money for just 15 years would cost $79,441, compared to $215,609 over 30 years, or nearly two-thirds less. The rub, of course, is the higher monthly payment.

(For more on choosing the right mortgage for you, see Bank Vs. Budget: How Much House Can You Afford? and Comparison Of A 30-Year Vs. A 15-Year Mortgage.)