15 vs 30 Year Loan Calculator

What a 15 vs 30 year loan comparison measures

Most people compare loans by monthly payment alone, and that is the trap. A 15 year loan and a 30 year loan differ in three numbers, and the payment is the least interesting of them:

• Monthly payment. The 15 year loan asks for more each month, usually 30 to 40 percent more.
• Total interest. This is where the gap explodes. A longer term means more payments, and each early payment is mostly interest.
• Speed to zero. The date your balance hits zero changes what the loan costs you per year of your life.

The calculator above takes the loan amount and a rate for each term, then prints the payment, the total paid, the total interest and the gap between them. It also runs one more scenario that most comparison tools skip: take the monthly difference and invest it instead, then ask whether the investment beats the interest you saved by shortening the loan.

The payment formula both terms share

Both loans use the same amortization formula. Only two inputs change: the number of months and, in real life, the rate, because lenders charge less for a shorter promise.

payment = loan x monthly rate x (1 + monthly rate)^months / ((1 + monthly rate)^months - 1)

The monthly rate is the annual rate divided by 12, and months is the term in years multiplied by 12. Total cost is then the payment multiplied by the number of payments, and total interest is total cost minus the amount borrowed. That is the whole machine. Everything surprising about the two terms falls out of how the early payments split between interest and principal, which is the next section.

Worked example: $300,000 at 6.0% versus 6.5%

Say you borrow $300,000. Lenders quote the 15 year loan about half a point cheaper, so imagine 6.0% for 15 years and 6.5% for 30 years. The first month's interest is the balance multiplied by the monthly rate: $300,000 x 6.0% / 12 = 1,500 on the short loan and $300,000 x 6.5% / 12 = 1,625 on the long one. Subtract that from each payment to see what pays down the loan.

The totals come straight from the payment: 180 x 2,531.57 = 455,682.60 and 360 x 1,896.20 = 682,632.00. Take away the $300,000 you borrowed and the interest is $155,682.60 versus $382,632.00, so $382,632.00 - 155,682.60 = 226,949.40 is the price of the longer term. The short loan puts $1,031.57 of its first payment into principal, which is 3.8 times what the 30 year loan manages with $271.20.

Where the interest gap comes from

The 30 year loan does not cost more because its rate is higher, though that helps. It costs more because for years the payment barely covers the interest. On the 30 year loan, $1,625 of the first $1,896.20 payment is interest, so 86 percent of your money never touches the balance. On the 15 year loan the split starts near 59/41 and improves every month.

Look at the same loan after five years:

The 30 year borrower has paid $94,605.18 - 79,921.52 = 14,683.66 more interest and still owes $52,806 more. That combination, more interest and less progress, is what people mean when they say the short loan builds equity faster. It is not a trick of the bank; it is arithmetic. Interest each month is the balance times the rate, so the only way to pay less of it is to push the balance down faster.

The invest-the-difference question

Here is the honest case for the 30 year loan. The payment is $635.37 lower. If you take that $635.37 every month and invest it, after 15 years you hold a pot of money while the 15 year borrower has a paid-off house and no pot. Whether that wins depends entirely on the return:

The bar to clear is the $226,949.40 of interest the short loan saves. Working it backwards, the invested gap needs about an 8.4% annual return to tie, before taxes. History says stock markets have beaten that over long runs, and history also says plenty of 15 year stretches did not. The plan only works if the gap does get invested; the monthly difference spent on dinner does not compound. Also note the cash cost: $635.37 x 180 = 114,366.60 of extra contributions over 15 years, which has to come from somewhere.

When the 15 year fits, and when the 30 fits

The right answer depends on income stability more than on math. Run your own numbers, then check them against this table:

One warning about stretching the budget for the shorter term: lenders approve you on the payment, not on your savings rate. A payment that eats half your take-home pay leaves no room for a roof, a repair or a layoff, and the 15 year loan is unforgiving in exactly those months. The 30 year loan with a voluntary extra payment keeps the same upside and hands you the escape hatch.

The scale changes with the loan size. On $400,000 at 6.1% versus 6.7%, the interest gap is $529,199.60 - 211,474.40 = 317,725.20. On $250,000 at 5.9% versus 6.4% it is $312,953.60 - 127,308.80 = 185,644.80. Bigger loan, bigger prize for the shorter term.

The middle path: extra payments on a 30 year loan

Option three gets ignored: take the 30 year loan and pay it like a 15 year. On the $300,000 example, add the $635.37 difference to the $1,896.20 payment and send $2,531.57 from day one. At 6.5% the loan dies in 191 months instead of 360, and the interest falls to $181,250.72, which is $382,632.00 - 181,250.72 = 201,381.28 saved against the plain 30 year schedule.

That is $181,250.72 - 155,682.60 = 25,568.12 more interest than the true 15 year loan, the price of the higher 6.5% rate. What you buy with that price is the right to drop back to $1,896.20 any month you need to. A mandatory $2,531.57 payment cannot shrink; a voluntary one can. Mark extra payments as principal only, or the servicer may park them as future payments and the whole plan does nothing.

Four mistakes people make when comparing the two terms

• Comparing at the same rate. Lenders price the 15 year lower. At an equal 6.5% on $300,000 the 15 year payment is $2,613.32, and 2,613.32 / 1,896.20 = 1.38, so the short loan costs about 38 percent more per month, not the 50 percent people guess.
• Ignoring what the payment gap gets spent on. The invest-the-difference case dies quietly if the gap funds lifestyle instead of a brokerage account.
• Forgetting the refinance myth. Taking the 30 year now and refinancing to 15 later assumes rates, your credit, home value and closing costs all cooperate in year eight. Nothing guarantees that.
• Reading the interest total as a loss you feel. It is real money, but it arrives across 30 years of rising incomes. Judge affordability by the monthly number against your budget today, then judge wealth by the totals.

Whichever side you land on, check the numbers with your own loan estimate rather than a rule of thumb, because a half point of rate moves every line in this article. The Consumer Financial Protection Bureau's owning a home tools and Freddie Mac's weekly rate survey are both good neutral references for the rate side of the comparison.