Mortgage Refinance Worked Example

The refinance question

The borrower started with a $590,000, 30-year fixed mortgage at 3.75%. Nearly seven years later, a lender offers a 15-year refinance at 2.8%. The refinance has a lower interest rate and a shorter term, but it also requires a higher monthly payment and $6,000 of closing costs paid upfront.

The useful comparison starts at the refinance decision date. Interest already paid explains how the current balance was reached, but it cannot be recovered. The practical question is whether the future refinance path is better than the future path of keeping the original loan.

Original loan inputs

• Original loan amount: $590,000
• Original interest rate: 3.75%
• Original term: 30 years
• Original start date: February 1, 2015
• Refinance decision date: January 1, 2022
• Scheduled payment override: empty

Leaving the override empty uses the standard fixed-rate payment formula. The scheduled principal-and-interest payment is $2,732.38 per month. A payment due on the decision date is included, so the historical part of the original-loan table contains 83 scheduled payments.

Past extra principal payments

The borrower also made two one-time extra principal payments before the refinance decision:

• June 1, 2020: $5,000
• March 1, 2021: $7,500

For each month, interest is calculated from the prior balance first. Scheduled principal is then applied, followed by that month's extra principal. The $12,500 of extra principal lowers the balance immediately and also reduces interest in later months.

Table 1: original loan path

Table 1 follows the original mortgage from its first payment through payoff. The highlighted row is the last payment on or before the refinance decision date. In this example, that row is payment 83 and it shows the loan's position at the decision point:

• Principal paid: $97,099.32
• Interest paid: $142,188.39
• Remaining balance: $492,900.68

After the highlighted decision row, Table 1 continues without restarting. It keeps the original 3.75% rate and $2,732.38 scheduled payment. With no future extra principal payments, the remaining original loan path produces:

• Future interest: $233,502.58
• Remaining payments: 266
• Projected payoff date: March 1, 2044

The original mortgage had 277 scheduled months left after payment 83, but the earlier extra principal payments shorten the projected payoff to 266 remaining payments.

Table 2: refinance offer

• New interest rate: 2.8%
• New term: 15 years
• Closing costs added to new loan: $0
• Closing costs paid upfront: $6,000
• Refinance start date: January 1, 2022

Table 2 starts a replacement loan at the refinance date. New principal equals the old payoff balance plus any closing costs added to the new loan. Because this example adds no closing costs to the loan, the new principal remains $492,900.68. The 15-year refinance produces:

• New monthly payment: $3,356.67
• Future interest: $111,300.03
• Payoff date: January 1, 2037

What the comparison says

From the decision date forward, refinancing reduces projected future interest by $122,202.55. The tradeoff is cash flow: the scheduled monthly payment rises by $624.29 because the new loan is repaid over 15 years instead of the remaining original schedule.

That higher payment is not a calculation error. More of each future payment goes toward principal, so the refinanced loan reaches payoff on January 1, 2037 instead of March 1, 2044.

How to read the balance chart

Both charts use months after the original loan start. For this 30-year example, the chart horizon extends from month 0 through month 360. The Table 1 balance line starts at $590,000 in month 0 and reaches payoff in month 349 because the irregular extra payments shortened the loan. The Table 2 balance line begins at the refinance point, month 83, with a balance of $492,900.68 and reaches payoff in month 263.

How to read the interest chart

The cumulative-interest chart includes already-paid interest so the two lifetime paths can be shown on one visual scale. Table 1 grows from $0 to $375,690.97 of lifetime interest. The Table 2 path begins at month 83 with the $142,188.39 of original-loan interest already paid. The refinanced loan alone adds $111,300.03, so the orange line ends at a combined original-plus-refinance interest total of $253,488.42.

Those lifetime totals are context. The decision result still compares only future interest after the refinance decision date, which is why the projected future interest savings are $122,202.55.

Closing-cost break-even

Closing-cost break-even asks when the future interest savings have recovered the closing costs paid upfront. For each month after the refinance starts, the calculator subtracts Table 2's cumulative interest from Table 1's cumulative interest and compares the savings with the $6,000 paid upfront.

In this example, cumulative interest savings recover the costs paid upfront in month 15, April 1, 2023. If closing costs paid upfront are zero, the calculator reports that recovery is immediate.

How to check both tables

1. Start each row with the prior row's ending balance.
2. Multiply that balance by 3.75% ÷ 12 in Table 1, or 2.8% ÷ 12 in Table 2, to get monthly interest.
3. Subtract interest from the scheduled payment to get scheduled principal.
4. Subtract scheduled principal and any extra principal from the prior balance to get the new ending balance.
5. In the final row, confirm that payment components are reduced as needed and the ending balance is exactly $0.00.

What this comparison does not include

This calculator compares one existing loan with one rate-and-term refinance offer. It does not rank multiple offers, calculate NPV or IRR, model taxes or escrow, predict home value, or discount future cash flows. Those omissions keep the month-by-month loan mechanics visible.