Loan Comparison Calculator

How it works

Each offer's monthly payment comes from the standard loan payment formula for its rate and term. Total interest is all the payments less the amount borrowed; total cost adds the upfront fees and points.

Most loans are not kept to the end: homes are sold and mortgages refinanced. So the calculator also works out what each offer costs over the months you expect to keep it: the payments you would make, plus the fees, plus the balance you would still owe and have to pay off, less the amount you borrowed. Paying points for a lower rate only pays off if you keep the loan long enough; this figure shows whether you do.

The APR spreads the fees over the loan the way federal Truth in Lending rules do (Regulation Z, Appendix J): it is the annual rate at which the monthly payments would repay the loan amount less the fees. An offer with no fees has an APR equal to its interest rate.

Formula

r = rate ÷ 12      n = term in months      k = min(holding months, n)
M = P × r × (1 + r)^n ÷ ((1 + r)^n − 1)
total interest = M × n − P          total cost = total interest + fees
balance after k = M × (1 − (1 + r)^−(n−k)) ÷ r
holding-period cost = M × k + fees + balance after k − P
APR = 12 × i, where M × (1 − (1 + i)^−n) ÷ i = P − fees

Example

Borrowing $300,000 for 30 years: Offer A is 6.5% with $2,000 of fees, Offer B is 6% with $8,000 of fees and points, Offer C is 6.75% with no fees. The payments are $1,896.20, $1,798.65 and $1,945.79; the APRs are 6.564%, 6.254% and 6.750%.

Kept for 7 years (84 months), Offer B costs $128,004.89, Offer A $132,529.88 and Offer C $135,809.14, so B is cheapest by $4,524.99. Kept for only 2 years, the no-fee Offer C is cheapest ($40,081.96 against A's $40,577.98 and B's $43,572.34): the points on B have not yet paid for themselves.

Excel's RATE example checks the APR method: a $9,600 loan at 0% for 48 months with $1,600 of fees has payments of $200 on $8,000 actually received, an APR of 9.24%.

Assumptions and limitations

• Rates are fixed, payments are monthly at the end of each month, and each loan fully amortizes over its term. Adjustable rates, balloon payments and interest-only periods are not modelled.
• All offers are for the same loan amount. Fees and points are paid upfront and are not added to the balance; if a lender finances them, add them to the loan amount and compare separately.
• Holding-period cost ignores the time value of money and any prepayment penalty, and it treats the remaining balance as repaid at the end of the period. It does not include taxes, insurance, PMI or escrow.
• The APR is the Regulation Z actuarial APR for a single advance with regular monthly payments and no odd first period, counting every fee you enter as a prepaid finance charge. The APR on a lender's disclosure may differ if some fees are excluded from the finance charge.
• Results are estimates for planning and are not financial, tax or legal advice. Compare against each lender's Loan Estimate or Truth in Lending disclosure.

Frequently asked questions