15 vs 30 Year Mortgage Calculator

On a $320,000 loan, a 15-year mortgage at 5.50% costs $2,614.67 a month and a 30-year mortgage at 6.25% costs $1,970.30. The 15-year loan charges $238,663.30 less interest.

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Your two loans side by side

15-year payment

$2,614.67

30-year payment

$1,970.30

Interest saved

$238,663.30

After 15 years, investing is short by

$42,396.40

The 15-year loan at 5.50% costs $2,614.67 a month, $644.37 more than the 30-year loan's $1,970.30 at 6.25%.

Over the full terms the shorter loan charges $238,663.30 less interest, $150,639.75 against $389,303.05; $215,427.04 of that comes from the shorter term alone, at the same 6.25% rate.

After 15 years the 15-year loan is paid off, while the 30-year loan still owes $229,791.25.

Investing the $644.37 difference at 6.00% would grow to $187,394.85, $42,396.40 short of that; it would need 8.34% a year to catch up.

Want the lower payment but a faster payoff? The extra payment calculator adds the difference to each payment. The mortgage payoff calculator finds the payment that ends it in your shorter term.

Your two loan offers

The shorter loan
The amount you borrow, not the home's price.
In whole years, such as 10, 15 or 20.
The interest rate on page 1 of its Loan Estimate, not the APR.
The longer loan
More years than the shorter term.
Page 1 of its Loan Estimate; the defaults are examples, not today's rates.
Investing the difference
How long you expect to keep the loan, up to the shorter term.
A yearly return you assume, after taxes and fees; it is not a promise.
Worked sheet for Your two payments and the investing result: how the investing against the extra owed of $42,396.40 is worked out, in 6 steps.Your two payments and the investing resultM = P × r × (1 + r)n ÷ ((1 + r)n − 1)fund = D × ((1 + i)m − 1) ÷ i15 years at 5.50%: r ≈ 0.00458333, (1 + r)180≈ 2.277584, M ≈ $2,614.6671 → $2,614.6730 years at 6.25%: r ≈ 0.00520833, (1 + r)360≈ 6.489166, M ≈ $1,970.2950 → $1,970.30difference = $2,614.67 − $1,970.30= $644.37 a monthafter 180 payments: $229,791.25 − $0.00= $229,791.25 more owed on the longer loani = 6.00% ÷ 12 = 0.005, fund = $644.37× ((1 + i)180 − 1) ÷ i ≈ $187,394.85short by $229,791.25 − $187,394.85 =$42,396.40
  1. 15 years at 5.50%: r ≈ 0.00458333, (1 + r)180 ≈ 2.277584, M ≈ $2,614.6671 → $2,614.67
  2. 30 years at 6.25%: r ≈ 0.00520833, (1 + r)360 ≈ 6.489166, M ≈ $1,970.2950 → $1,970.30
  3. difference = $2,614.67 − $1,970.30 = $644.37 a month
  4. after 180 payments: $229,791.25 − $0.00 = $229,791.25 more owed on the longer loan
  5. i = 6.00% ÷ 12 = 0.005, fund = $644.37 × ((1 + i)180 − 1) ÷ i ≈ $187,394.85
  6. short by $229,791.25 − $187,394.85 = $42,396.40
How $2,614.67, $1,970.30 and $42,396.40 are worked out

The invested difference against the extra owed on the longer loan

The invested difference against the extra owed on the longer loan, year 1 to 15: the extra owed on the longer loan rises from $10,378.88 to $229,791.25 and the invested difference rises from $7,948.67 to $187,394.85.$0$100k$200k$300k151015YearExtra owedInvested differenceThe invested difference against the extra owed on the longer loan, year 1 to 15: the extra owed on the longer loan rises from $10,378.88 to $229,791.25 and the invested difference rises from $7,948.67 to $187,394.85.$0$100k$200k$300k151015YearExtra owedInvested difference
At 6.00% the invested difference stays below the extra owed through year 15, ending $42,396.40 short.

Extra interest on the longer loan against what the fund earns

Extra interest on the longer loan against what the fund earns, year 1 to 15: the extra interest on the longer loan rises from $2,646.44 to $113,805.50 and the fund's earnings rises from $216.23 to $71,408.25.$0$50k$100k$150k151015YearExtra interestFund earningsExtra interest on the longer loan against what the fund earns, year 1 to 15: the extra interest on the longer loan rises from $2,646.44 to $113,805.50 and the fund's earnings rises from $216.23 to $71,408.25.$0$50k$100k$150k151015YearExtra interestFund earnings
By year 15 the 30-year loan has charged $113,805.50 more interest than the 15-year loan, while the fund has earned $71,408.25.

Year by year: what each loan owes and the invested difference

YearShorter loan owesLonger loan owesExtra owed on the longer loanInvested differenceFund minus extra owed
1$305,871.32$316,250.20$10,378.88$7,948.67-$2,430.21
2$290,945.67$312,259.20$21,313.53$16,387.59-$4,925.94
3$275,178.09$308,011.49$32,833.40$25,347.01-$7,486.39
4$258,521.11$303,490.56$44,969.45$34,859.02-$10,110.43
5$240,924.56$298,678.84$57,754.28$44,957.71-$12,796.57
6$222,335.41$293,557.62$71,222.21$55,679.27-$15,542.94
7$202,697.68$288,106.99$85,409.31$67,062.12-$18,347.19
8$181,952.23$282,305.76$100,353.53$79,147.03-$21,206.50
9$160,036.58$276,131.39$116,094.81$91,977.31-$24,117.50
10$136,884.72$269,559.87$132,675.15$105,598.93-$27,076.22
11$112,426.91$262,565.66$150,138.75$120,060.71-$30,078.04
12$86,589.50$255,121.57$168,532.07$135,414.46-$33,117.61
13$59,294.65$247,198.67$187,904.02$151,715.19-$36,188.83
14$30,460.14$238,766.17$208,306.03$169,021.32-$39,284.71
15$0.00$229,791.25$229,791.25$187,394.85-$42,396.40

At 6.00% the fund stays below the extra owed in every year shown: $2,430.21 short after year 1 and $42,396.40 after year 15.

Paying the longer loan like the shorter one

PlanMonthly paymentPaymentsTotal interestOwed at the end of the shorter term
15-year loan$2,614.67180$150,639.75$0.00
30-year loan, paying $2,614.67$2,614.67196$190,640.11$38,350.29
30-year loan, paid off in 15 years$2,743.75180$173,876.01$0.00
30-year loan as scheduled$1,970.30360$389,303.05$229,791.25

Paying $2,614.67 a month on the 30-year loan still leaves $38,350.29 owed after 15 years, and it takes 196 payments, the last $779.46. To finish the 30-year loan in 15 years at 6.25% takes $2,743.75 a month, with a last payment of $2,744.76.

Your two loans, line by line on the Loan Estimate

Line on the formShorter loanLonger loan
Monthly principal & interest (page 1)$2,614.67$1,970.30
In 5 Years: principal and interest paid (page 3)$156,880$118,218
In 5 Years: principal you will have paid off (page 3)$79,075$21,321
Total Interest Percentage, TIP (page 3)47.075%121.657%

The form's In 5 Years total also counts mortgage insurance and loan costs, which this table leaves out, so yours will be higher; compare the principal line instead. The TIP here leaves out prepaid interest, which the form counts, and the form drops a TIP's trailing zeros.

If you sell or refinance sooner

Loan keptExtra owed on the longer loanInvested differenceFund minus extra owedReturn the fund needs
1 year$10,378.88$7,948.67-$2,430.21over 30.00%
3 years$32,833.40$25,347.01-$7,486.3922.74%
5 years$57,754.28$44,957.71-$12,796.5715.44%
7 years$85,409.31$67,062.12-$18,347.1912.37%
10 years$132,675.15$105,598.93-$27,076.2210.09%
15 years (yours)$229,791.25$187,394.85-$42,396.408.34%

Kept 1 year, the fund would need over 30.00% a year to catch up; kept 15 years, 8.34%.

How a shorter mortgage term saves interest

A mortgage's term is the number of years you take to repay it. The CFPB's page on the kinds of home loans says "The term of your loan is how long you have to repay the loan." At the same rate, fitting the same amount into fewer payments makes the monthly payment larger, or at times the same once rounded to the cent. Each month the lender charges interest on the balance you still owe. The larger payment pays the balance down faster, so the interest charged on it falls faster too.

The same CFPB page gives two reasons a shorter term can cost less: "You are borrowing money and paying interest for a shorter amount of time", and "The interest rate is usually lower—by as much as a full percentage point". So this page takes each loan at its own rate. Enter the interest rate from page 1 of each Loan Estimate, not the APR on page 3, which also counts fees.

Each payment is rounded to the cent, and so is each month's interest, the way a lender's schedule works. The last payment takes up what the rounding leaves, so it differs from the others by whatever the rounding has added up to. The default 15-year loan's last payment is $2,613.82, and the 30-year loan's is $1,965.35.

The longer loan's lower payment leaves money free each month. This page asks what happens if you invest that difference instead of paying the loan down. After the years you choose, it sets the fund against the extra balance the longer loan still owes. The return is your assumption: the SEC's page on risk warns that "All investments involve some degree of risk."

Where the saving comes from: the term or the rate

Split the default saving into its two causes. A 15-year loan at the 30-year loan's own 6.25% would cost $2,743.75 a month and charge $173,876.01 of interest. So the shorter term alone saves $215,427.04 of interest, 90.26% of the whole saving. The 5.50% rate saves the other $23,236.26 and cuts the payment by $129.08. On these loans, repaying faster matters far more than the lower rate.

Why investing the difference has to beat the loan's rate

Each dollar you invest instead of repaying leaves a dollar of balance that the loan keeps charging interest on. So on the default $320,000 loans the fund must earn at least the 6.25% rate to keep up, and more when the shorter loan's rate is lower. With both loans at 6.25%, it needs 6.26% a year over 15 years, a hundredth of a point above the rate. With the 15-year loan at 5.50%, the longer loan also charges 0.75 percentage points more on its whole balance, and the fund needs 8.34%.

A mortgage's fixed rate is set in your contract, while a fund's return is not. The SEC's page on risk says large company stocks "have lost money on average about one out of every three years." Paying the loan down earns its rate for certain; investing has to earn more than that to be worth the risk.

Taking the 30-year loan and paying it like a 15-year loan

Paying the 15-year payment on the 30-year loan does not finish it in 15 years. At 6.25% it takes $2,743.75 a month, and $2,744.76 for the last payment, to finish in 15 years, so $2,614.67 leaves $38,350.29 owed after 180 payments. It takes 196 payments, the last $779.46, and $190,640.11 of interest. That is $40,000.36 more than the true 15-year loan charges.

What you buy with that extra interest is the right to drop back to $1,970.30 in a hard month. The table of plans above works this out for your own loans. The extra payment calculator tries other amounts; it works without rounding to the cent, so its interest total is $0.74 higher.

Video walkthrough

A 3-minute walkthrough of what a shorter mortgage term saves, and whether investing the lower payment's difference catches up.

Mortgage Term Comparison: Is a Shorter Loan Worth the Higher Payment?
Read the transcript

Is the shorter loan worth it?

0:00 Is a 15-year mortgage worth the higher payment?

0:03 On this loan, it costs about $640 more a month than a 30-year loan.

0:10 In return, it charges about $239,000 less interest.

0:16 That's a big saving, but the longer loan frees up cash every month that you could invest instead.

0:22 Would that catch up?

Where the saving comes from

0:24 First, why is the shorter loan so much cheaper?

0:28 Its rate is lower, and you pay interest for half as many years.

0:32 Which counts for more?

0:33 Give both loans the longer loan's rate.

0:36 The shorter term on its own still saves about $215,000, or about 90% of the saving.

0:44 The lower rate saves the rest.

Investing the difference instead

0:47 Now the other plan: take the longer loan, and invest the difference every month at 6% a year.

0:54 Over the same years, the fund grows to about $187,000.

1:00 But by then the shorter loan is paid off, and the longer one still owes about $230,000.

1:08 So the fund comes up about $42,000 short.

Why the fund has to beat the loan

1:13 Why does it fall short?

1:14 Every dollar you invest is a dollar you still owe at the loan's rate.

1:19 Year after year, the longer loan's extra interest runs ahead of what the fund earns.

1:25 To catch up, the fund would need to earn about 8.3% a year.

1:30 At 10%, it would come out about $37,000 ahead.

1:35 But no return is promised.

1:37 The SEC's page on risk warns that all investments involve some degree of risk.

1:43 A fixed loan rate, by contrast, never changes.

Selling sooner, or paying extra

1:48 Time matters too.

1:49 If you sell sooner, the fund has less time to grow.

1:53 Kept 5 years, it would need about 15% a year.

1:57 What if you take the longer loan, but pay it like the shorter one?

2:01 Paying the shorter loan's payment still leaves about $38,000 owed after 15 years, because of its higher rate.

2:10 You'd also pay more interest than on the real shorter loan.

2:14 What that buys is a way out: in a tight month, you can drop back to the lower payment.

Compare your own offers

2:20 To compare your own offers, take the interest rate from page 1 of each Loan Estimate.

2:26 Not the APR, which counts fees too.

2:30 Say you're refinancing $260,000.

2:34 Type the shorter loan's rate, then the longer loan's term, 25 years here, and its rate.

2:40 The results change as you type.

2:43 Here the shorter loan saves about $114,000 of interest.

2:48 The table by year downloads as a spreadsheet file, and the copy link button saves both offers in one address.

2:56 So the shorter loan saves the most interest, and investing the difference wins only above the break-even return, which no one can promise.

3:05 Try your own offers at fastcalc.us.

Mortgage term comparison formulas

r = rate ÷ 12          n = term in years × 12
M = P × r × (1 + r)^n ÷ ((1 + r)^n − 1), rounded to the cent;  M = P ÷ n when r = 0
interest each month = balance × r, rounded to the cent; the last payment is the balance plus its interest
difference D = M(shorter) − M(longer)          extra owed = balance(longer) − balance(shorter) after m months
fund = D × ((1 + i)^m − 1) ÷ i, rounded to the cent, with i = return ÷ 12;  fund = D × m when i = 0
fund minus extra owed = fund − extra owed;  break-even = the lowest return, to 0.01%, at which it is 0 or more
P loan amount · M payment · n payments · r monthly rate · m months compared · i monthly return

Worked examples

A 10-year loan. Compare $320,000 over 10 years at 5.25% with the 30-year loan at 6.25%, over 10 years. The 10-year loan costs $3,433.33 a month and charges $297,302.79 less interest. After 10 years it is paid off, while the 30-year loan still owes $269,559.87. Investing the $1,463.03 difference at 6.00% would reach $239,760.40, so it would need 8.13% a year to catch up.

Selling after 7 years. Keep the default loans but compare after 7 years. The 30-year loan then owes $85,409.31 more than the 15-year loan. The fund at 6.00% holds $67,062.12, which is $18,347.19 short. It would need 12.37% a year to catch up, far more than over 15 years.

Check your two Loan Estimates

Ask each lender for a Loan Estimate for each term. The CFPB's page on the kinds of home loans advises: "Always compare official loan proposals, called Loan Estimates, before making your decision." Page 1 of each one gives the interest rate and the monthly principal and interest. Under 12 CFR 1026.37(b)(3), that payment is "The initial periodic payment amount that will be due under the terms of the legal obligation". Compare it with this page's payment.

Page 3 has a Comparisons table. Its In 5 Years line gives "The principal scheduled to be paid through the end of the 60th month after the due date of the first periodic payment" (12 CFR 1026.37(l)(1)(ii)). That amount is rounded to the whole dollar under 12 CFR 1026.37(o)(4)(i)(A). For the default loans it is $79,075 on the 15-year loan and $21,321 on the 30-year loan. The total paid on the same line also counts mortgage insurance and loan costs, which this page leaves out.

The same table gives the Total Interest Percentage, the interest over the whole term as a share of the loan (12 CFR 1026.37(l)(3)). It is shown to three decimals under 12 CFR 1026.37(o)(4)(ii), so the default loans read 47.075% and 121.657%. The CFPB's answer on the TIP says "The TIP is most useful as a comparison point between different Loan Estimates." The official comment 37(l)(3)-1 also counts prepaid interest, which this page leaves out, so your form's TIP can differ a little.

You can test this page against the CFPB's sample Loan Estimate, form H-24(B), for $162,000 over 30 years at 3.875%. It prints a monthly principal and interest of $761.78 and $15,773 of principal paid off in 5 years. Entered as the longer loan, this page gives the same $761.78, and $15,772.58 of principal, which rounds to $15,773. Over 15 years at the same 3.875%, that loan would cost $1,188.17 a month and pay off $43,952 in 5 years.

When your situation is different

If you sell or refinance within a few years

Investing the difference has less time to grow when you keep the loan a short time. On the default loans, after 5 years the 30-year loan owes $57,754.28 more, and the fund at 6.00% holds $44,957.71. To catch up it would need 15.44% a year. The extra interest starts on the whole balance at once, while the fund starts at $0.00. The table of horizons above gives the hurdle for your loans.

If you are refinancing

A new loan starts its term again. Say you owe $260,000 with 25 years left. Enter $260,000, a 15-year term at 5.25% and a 25-year term at 5.75%. The 15-year loan costs $2,090.08 a month against $1,635.68 and charges $114,486.99 less interest. A new 30-year loan would add five more years of payments instead. The mortgage refinance calculator adds closing costs and finds when they pay back.

If you pay every two weeks

A year has 52 weeks, so half a payment every two weeks makes 26 halves, or 13 full payments instead of 12. Over a year that is the same as adding a twelfth of a payment each month. On the default 30-year loan, $2,134.49 a month repays it in 293 payments and saves $85,617.89 of interest. That is far short of the 15-year loan's 180 payments. The biweekly mortgage calculator works out a biweekly plan for your loan.

If the shorter term has the higher rate

The CFPB's page on the kinds of home loans says a shorter term's rate is "usually lower", not always, so your shorter-term offer may carry the higher rate. Take a 20-year loan at 6.75% against the 30-year loan at 6.25%. The 20-year loan still charges $125,342.28 less interest over its term, but it costs $462.86 more a month. After 15 years, investing that difference at 6.00% beats the extra owed by $28,433.24, and 3.14% a year would have been enough.

Assumptions and limits

  • Both loans have fixed rates and monthly payments, and the first payment is due a month after closing.
  • Interest is a twelfth of the yearly rate each month, on the balance owed, not figured by the day.
  • Payments and interest are rounded to the cent, and the last payment takes up the difference. Regulation Z's official comment 17(c)(3)-1 notes that "the amount of the last payment may require adjustment to account for the rounding of the other payments to whole cents."
  • The figures are principal and interest only. Property tax, homeowners insurance and mortgage insurance are left out; the mortgage payment calculator adds them to the payment. Do not add them to the loan amount, which would charge interest on them.
  • Closing costs and points are left out. Points and lender fees count in each Loan Estimate's APR instead.
  • The difference is invested at the end of each month and grows at the return you enter, compounded monthly, with no taxes, fees or losses.
  • The 5.50% and 6.25% defaults are examples, not today's rates. Their 0.75-point gap is within the full percentage point the CFPB names.
  • Loan amounts run from $1,000 to $100,000,000 and rates from 0% to 30% with up to three decimals. The shorter term runs from 1 to 39 years and the longer from 2 to 40, and the years compared run up to the shorter term.

These figures are estimates for learning and planning, not financial, tax, legal or investment advice. Terms of use.

What to do with your result

Start from the payment you can keep up for the whole term. The 15-year loan's $2,614.67 is principal and interest only. Add tax and insurance in the mortgage payment calculator, then check the total against your income in the home affordability calculator.

Get a Loan Estimate for each term; the CFPB's Loan Estimate explainer says to "Request multiple Loan Estimates from different lenders so you can compare and choose the loan that's right for you." On page 3, the principal paid off in 5 years should read $79,075 and $21,321 for the default loans. If yours differ, ask the lender why. The loan amortization calculator lists every payment of the shorter loan.

If the 15-year payment feels tight, take the 30-year loan and pay extra. Paying $2,743.75 a month, and $2,744.76 for the last payment, finishes the default 30-year loan in 15 years and still lets you fall back to $1,970.30. The mortgage payoff calculator finds that payment for your loan.

Invest the difference only if you expect to beat the break-even return after taxes and fees. On the default loans that is 8.34% a year over 15 years. Before choosing the longer loan to invest, the pay off debt or invest calculator weighs paying the loan down against investing.

15-year and 30-year mortgage questions

How much more is a 15-year mortgage payment than a 30-year?

On $320,000 at the default rates, the 15-year payment is $644.37 more a month. At the same 6.25% rate on both loans, the gap would be $773.45. The 15-year loan's lower 5.50% rate narrows it by $129.08.

How much interest does a 15-year mortgage save?

On the default loans, the 15-year loan charges $150,639.75 of interest and the 30-year loan $389,303.05. That is the $238,663.30 difference shown in the results, with each loan at its own rate.

Is it better to take a 30-year mortgage and invest the difference?

Only if the fund beats the break-even return. On the default loans over 15 years, investing the difference at 4.00% leaves you $71,217.92 behind the 15-year loan, and at 8.00% $6,814.60 behind. At 10.00% you would be $37,281.01 ahead, but no fund's return is certain.

Can I pay off a 30-year mortgage in 15 years?

Yes, if your loan has no prepayment penalty and you pay enough. The CFPB's answer on prepayment penalties says "Not all mortgages have a prepayment penalty." On the default loan, $2,743.75 a month, with a last payment of $2,744.76, repays it in 15 years.

Should I enter the interest rate or the APR?

The interest rate. The CFPB's answer on rates and APRs says the APR "reflects the interest rate, any points, mortgage broker fees, and other charges that you pay to get the loan." Entering a 5.75% APR in place of a 5.50% rate makes the 15-year payment $42.64 too high.

Is a 20-year mortgage a good middle ground?

It can be. On $320,000, a 20-year loan at 5.875% costs $2,269.56 a month, $299.26 more than the 30-year loan, and charges $164,607.29 less interest. Over 20 years, investing that difference would need 7.97% a year to catch up.

How fast do you build equity on a 15-year vs a 30-year mortgage?

On the default loans, much faster on the shorter loan, before any change in the home's value. Half the 15-year loan is repaid after payment 109. The 30-year loan takes until payment 255. After 10 years the 15-year loan owes $136,884.72 and the 30-year loan $269,559.87.

Sources

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