What a change in rate is worth
Mortgage shopping is usually a negotiation over fractions of a percentage point. This calculator converts those fractions into money, which is the only form in which they can be judged.
Over thirty years, small rate differences accumulate into sums comparable to a car or a year of income. The comparison below makes that concrete.
The formula behind the number
An amortising loan is repaid in equal instalments. Each one covers the interest that accrued since the last payment, and whatever is left reduces the balance. The instalment that brings the balance to exactly zero on the final payment is:
Here P is the amount borrowed, i is the monthly rate (the annual rate divided by 12) and n is the number of payments. Nothing else enters the calculation, which is why two lenders quoting the same three inputs must arrive at the same instalment.
Worked example: $350,000 at 6.5% over 30 years
The calculator opens on this scenario, so you can follow every step:
- Amount borrowed: $350,000
- Annual rate: 6.5%, so the monthly rate is 6.5 ÷ 12 = 0.5417%
- Term: 30 years, so n = 30 × 12 = 360 payments
Paying $2,212.24 every month for 360 months comes to $796,406. Subtract the $350,000 you actually borrowed and the cost of the credit is $446,406, or 128% of the sum borrowed.
Where each payment goes
The instalment never changes, but its composition does. The first payment carries $1,895.83 of interest and only $316.40 of principal. By payment 180 the split has moved to $1,380.11 interest against $832.13 principal.
| Payment | Instalment | Interest | Principal | Balance |
|---|---|---|---|---|
| 1 | $2,212.24 | $1,895.83 | $316.40 | $349,684 |
| 2 | $2,212.24 | $1,894.12 | $318.12 | $349,365 |
| 3 | $2,212.24 | $1,892.40 | $319.84 | $349,046 |
| 180 | $2,212.24 | $1,380.11 | $832.13 | $253,957 |
| 360 | $2,212.24 | $11.92 | $2,200.32 | $0.00 |
A lower rate does not only reduce the payment. It shifts the whole schedule toward principal, so equity builds faster from the first month.
What moves the answer most
Two levers change the total, and they do not pull with equal force.
Add one percentage point to the rate and the instalment goes from $2,212.24 to $2,447.25, which is $84,605 more over the full term. Cut 5 years off the term instead and the instalment rises to $2,363.23, but total interest falls from $446,406 to $358,968. Paying points to buy the rate down is worth it only if you keep the loan long enough to recover the upfront cost — check the break-even before agreeing.
What this calculator leaves out
Discount points, lender credits and closing costs are excluded. A rate is only comparable to another rate once those are folded in, which is what APR is for.
Related calculators
- APR calculator — the rate with fees included
- Points calculator — whether buying the rate down pays off
- Refinance break-even — how long until a new rate repays its costs