ABC Tools

Mortgage Refinance, Explained

After reading this you can tell whether a refinance offer actually saves you money, work out the month its closing costs pay for themselves, and spot the trap where a lower payment hides a higher lifetime cost.

What refinancing is and one quick example

Refinancing means replacing your current mortgage with a new one. You borrow enough to pay off the old balance, then repay the new loan on new terms: a new rate, a new number of years, and a set of closing costs you pay up front to make it happen.

The decision comes down to a trade. You pay closing costs now. In return you get a lower monthly payment, or a shorter term, or both. The question is whether the future savings outweigh the cost you pay today.

Here is the shape of it. Suppose you owe 250000 at 7.5% with 300 months left. Your payment is about 1847 per month. A new 25 year loan at 6% would cost about 1611 per month. That is 236 less each month. If the refinance costs 4000 to arrange, you recover that in roughly 17 months, then the saving is yours. The rest of this article shows exactly where those numbers come from.

When it helps and when it does not

Refinancing tends to pay off when the rate drop is large, you plan to stay in the home long enough to pass the break-even month, and the closing costs are modest relative to the monthly saving.

It often disappoints in three situations. First, when you sell or move before break-even, so you never recoup the costs. Second, when the new rate is barely below the old one, so the monthly saving is small and break-even is years away. Third, when you stretch the term back out to 30 years to shrink the payment, which can raise the total interest even though each month feels cheaper.

A lower monthly payment is not the same as a lower total cost. Restarting a fresh 30 year term at a lower rate can still make you pay more interest over the life of the loan, because you are borrowing for longer. Always check the lifetime number, not just the payment.

The formula and the intuition

Every fixed-rate mortgage payment comes from the same annuity formula. For a balance P, a monthly rate i, and a number of months n, the payment is:

M = P \cdot \frac{i (1 + i)^n}{(1 + i)^n - 1}

Here M is the monthly payment, P is the amount owed, i is the annual rate divided by 12, and n is the total months. A rate of 7.5% gives i = 0.075 / 12 = 0.00625.

The intuition: the numerator grows the payment with the interest rate, and the denominator spreads it across the months. More months in n means a bigger denominator, so a smaller payment, but you make more of those payments, so more total interest.

Lifetime cost is simpler. Multiply the payment by the number of months, then add the closing costs for the new loan:

C = M \cdot n + \text{costs}

To compare two loans fairly, compute C for each and look at the difference. The break-even month is where the money you have saved on payments first equals the closing costs you paid:

t_{be} = \frac{\text{costs}}{M_{old} - M_{new}}

where M_{old} - M_{new} is the monthly saving. If that saving is zero or negative, break-even never arrives and the refinance only makes sense for other reasons, such as ending an adjustable rate.

A worked example using the demo data

250,000 at 7.5% versus 6% over 25 years

These are the tool's default values, so you can reproduce every figure with one click on the demo button.

  1. Current loan. P = 250000, i = 0.075/12 = 0.00625, n = 300. Then (1.00625)^{300} \approx 6.520, so M_{old} = 250000 \cdot (0.00625 \cdot 6.520) / (6.520 - 1) \approx 1846.6.
  2. New loan. P = 250000, i = 0.06/12 = 0.005, n = 300 (25 years). Then (1.005)^{300} \approx 4.465, so M_{new} = 250000 \cdot (0.005 \cdot 4.465) / (4.465 - 1) \approx 1610.7.
  3. Monthly saving. 1846.6 - 1610.7 = 235.9 per month.
  4. Break-even. 4000 / 235.9 \approx 16.96, so about month 17.
  5. Lifetime cost, current. 1846.6 \times 300 = 553980.
  6. Lifetime cost, new. 1610.7 \times 300 + 4000 = 483210 + 4000 = 487210.
  7. Lifetime saving. 553980 - 487210 = 66770.

So this refinance lowers the payment by about 236, pays for its 4000 in roughly 17 months, and saves about 66,770 over the full 25 years. Both terms are 300 months here, so the lower rate helps on every measure. That is the clean case.

The refinance is lower on both the monthly payment and the lifetime cost. The lifetime bars are shown in thousands so both measures fit one axis.

Reading and interpreting the results

The calculator gives you three numbers. Read them together, not one at a time.

Payment change
The difference in monthly payment. Negative means cheaper each month. In the demo it is about -236.
Break-even month
When accumulated savings match the closing costs. Stay past this month and you come out ahead. In the demo it is month 17.
Lifetime saving
Total interest and cost saved across the whole new term, closing costs included. In the demo it is about 66,770.

Watch what happens when the new term is longer than the months left on the old loan. If you have 300 months left but take a fresh 360 month loan, the payment falls further, but you now make 60 extra payments. The lifetime saving can shrink or flip to a loss even while the payment change looks great.

Cumulative monthly savings rise by about 236 each month. They cross the 4,000 closing cost at the marked month 17, which is the break-even point.

With the demo figures, a monthly saving of 236 recovers 4,000 in closing costs in about 17 months. Raise the closing costs to 8,000 and break-even doubles to about 34 months. Shrink the rate gap so the saving is only 60 per month, and break-even jumps past 66 months.

Common mistakes

The errors below turn a sensible comparison into a misleading one.

  • Comparing new payment to old payment while ignoring the term. A 30 year refinance against a loan with 22 years left is not like for like. Match the terms, or read the lifetime cost, or both.
  • Forgetting the closing costs in the lifetime number. The costs are real money. The tool adds them to the new loan's lifetime cost so the comparison is honest.
  • Rolling costs into the balance and ignoring the interest on them. If you finance the 4000 instead of paying cash, you pay interest on it for years. That raises the true cost above 4000.
  • Chasing a tiny rate drop. Dropping from 7.5% to 7.3% on 250000 saves roughly 33 a month. Against 4000 of costs, break-even is over 120 months. If you might move sooner, you lose.
  • Treating the result as advice. These figures ignore your tax situation, private mortgage insurance, and the value of cash you keep instead of spending on costs.

Ask the lender for the total closing costs in writing, then run the number twice: once assuming you stay to the end, and once assuming you move at your realistic horizon, say 5 years. If the refinance wins in both, it is a strong case.

Related tools

To build the full picture around a refinance, these calculators help:

Frequently asked questions

How much does the rate need to drop for refinancing to be worth it?

There is no fixed threshold, because it depends on your balance, costs and how long you stay. As a check, compute the monthly saving and divide the closing costs by it. On 250000, dropping from 7.5% to 6% saves about 236 a month and recovers 4000 in 17 months. Dropping only to 7.3% saves about 33 and takes over 10 years.

Why does my payment fall but my lifetime cost rise?

Because you extended the term. Stretching from 22 years remaining back to a fresh 30 years spreads the balance over more months, so each payment is smaller, but you make many more of them. The extra months of interest can outweigh the lower rate. Check the lifetime saving figure to catch this.

Should I count closing costs I roll into the loan?

Yes. If you add the 4000 to the balance instead of paying cash, you owe interest on it for the whole term. Treat the new balance as 254000 in that case, which raises both the payment and the lifetime cost.

What is the break-even month exactly?

It is the month when your accumulated monthly savings first equal the closing costs. Before it, you are behind because you paid the costs. After it, every month is pure gain. In the demo, 4000 / 235.9 = 16.96, so month 17.

Is this calculator financial advice?

No. It is an educational estimate. It leaves out taxes, insurance changes, and the opportunity cost of the cash you spend on closing. Talk to a qualified adviser before deciding.

Try it yourself in the tool

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