First Home Loan Comparison: Compare Payments and Costs

A first home loan comparison calculator estimates the monthly principal-and-interest payment and total interest for a mortgage using the loan amount, annual percentage rate (APR), and term you enter. It does not compare lender offers automatically; use each offer’s quoted figures as inputs, then compare the results alongside fees and other costs.

Formula

The calculator treats the loan as a fixed-rate balance repaid through equal monthly payments. It calculates the payment using the standard amortizing-loan formula, then multiplies that rounded payment by the number of monthly payments to find the amount repaid and subtracts the principal to estimate interest.

• p is the amount borrowed, in dollars.
• apr is the annual percentage rate entered as a percentage, not a decimal; for example, enter 8 for 8%.
• r is the monthly rate as a decimal: apr / 1200.
• yrs is the loan term in years.
• n is the number of monthly payments: yrs × 12.
• pmt is the monthly principal-and-interest payment in dollars, rounded to cents.
• int is estimated total interest in dollars over the full term.

In symbols: pmt = p × r / [1 − (1 + r)⁻ⁿ], where r = apr / 1200 and n = yrs × 12. Then int = pmt × n − p. The payment expression uses the standard formula without intermediate rounding; the displayed payment is rounded to cents, and total interest uses that displayed, rounded payment.

Worked Example

Using the calculator’s defaults, the principal is $20,000, APR is 8%, and the term is 5 years.

1. Convert APR to a monthly decimal rate: r = 8 / 1200 = 0.0066667.
2. Find the number of payments: n = 5 × 12 = 60.
3. Substitute into the payment formula: pmt = 20,000 × 0.0066667 / [1 − (1.0066667)⁻⁶⁰].
4. The monthly payment is approximately $405.53 after rounding to cents.
5. Total of rounded payments = $405.53 × 60 = $24,331.80.
6. Estimated total interest = $24,331.80 − $20,000 = $4,331.80.

Assumptions

• The interest rate stays fixed for the whole term.
• Payments are equal, made monthly, and paid at the end of each monthly period.
• Interest accrues monthly at APR / 12; the model does not reproduce every lender’s day-count or payment-processing method.
• Fees, property taxes, homeowners insurance, mortgage insurance, escrow deposits, and other charges are not included.

How to Compare First Home Loan Offers

For a useful comparison, enter the same proposed principal and term for each offer, together with the rate or APR specified in its disclosure. If the offers have different rates, the outputs show how those inputs affect the scheduled payment and modeled interest. Keep the assumptions consistent: changing the loan amount or term at the same time makes it harder to identify which difference explains a changed result.

A mortgage offer can include costs that this calculator does not capture. Request or review each offer’s written loan estimate and disclosure, and note the quoted payment components, fees, rate type, and whether the rate is fixed or can change. APR may reflect certain costs as well as interest, depending on the offer and applicable disclosure method; it is not necessarily identical to the note rate used to calculate the scheduled principal-and-interest payment. Use the figure that matches the calculation you intend to model, and verify the lender’s own payment estimate.

• Compare like with like: hold the amount borrowed and repayment period constant when isolating rate effects.
• Separate payment from cash needed: a monthly principal-and-interest estimate is not the same as upfront closing costs or total monthly housing expenses.
• Check the rate structure: a variable or adjustable rate may not stay at its initial level, so a fixed-rate estimate cannot forecast later payments.
• Look for included costs: lender disclosures can show charges or payment items absent from this arithmetic.

Reading the Results and Their Limits

The monthly payment is an estimate of principal and interest only, not a statement of what a lender will collect each month. A real payment may also include taxes, insurance, mortgage insurance, association charges, or escrow amounts, depending on the arrangement. Likewise, estimated total interest assumes every scheduled payment is made as modeled and the loan is not paid early, modified, or otherwise changed.

Rounding matters in long-term comparisons. The calculator rounds the monthly payment to cents and uses that rounded amount for its interest total, as specified by the formula. A lender’s schedule may differ slightly because of its precise payment dates, rounding conventions, disbursement timing, or fees. Treat small differences as a prompt to check the underlying assumptions rather than as proof that an offer is inaccurate.

The term also affects the comparison: a longer repayment schedule generally has more payment periods, while the payment formula spreads repayment across those periods. This calculator does not determine eligibility, predict future rates, estimate a home’s value, or tell you how much you can borrow. Enter figures supplied for the offer being considered, rather than treating the default example as a market quote or personal estimate.

Common Comparison Mistakes

• Entering 0.08 instead of 8: APR is entered in percentage units, so 8 represents 8%.
• Comparing different loan sizes: a smaller payment may simply reflect a smaller principal, not a lower borrowing cost.
• Treating principal and interest as the full housing payment: taxes, insurance, and other items are outside the output.
• Assuming APR and note rate are interchangeable: check which rate the payment calculation uses and what the disclosure’s APR includes.
• Reading total interest as total cost: it excludes principal and any charges not represented in the inputs.

Frequently Asked Questions

What should I enter for a first home loan comparison?
Enter the proposed amount borrowed, the relevant annual rate as a percentage, and the term in years. Use figures from the written offer and keep the amount and term consistent when comparing rates.

Does the monthly payment include property tax and insurance?
No. The result includes modeled principal and interest only. Check the offer documents for any taxes, insurance, mortgage insurance, escrow, or other payment items.

Is APR the same as the mortgage interest rate?
Not necessarily. The note rate is used to determine scheduled interest, while APR may incorporate certain costs under the applicable disclosure method. Confirm which figure belongs in the calculation and compare disclosures carefully.

Why does a lender’s payment differ from this estimate?
The lender may use different timing or rounding, and its quoted payment may include items this calculator omits. A variable rate, fees, or other loan features can also make the offer differ from the fixed-rate model.

Can I use this calculator to decide what I can afford?
No. It estimates loan arithmetic, not household affordability, approval, or the complete cost of owning a home. Those depend on personal circumstances and costs not represented here.

This result is an estimate for education; the lender’s disclosure gives the exact figures.

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in p | Loan amount | $ | 20000 | 1 | 100000000
in apr | Interest rate (APR) | % | 8 | 0.01 | 100
in yrs | Loan term | years | 5 | 0.0833 | 50
out pmt | Monthly payment | $ | p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -(yrs * 12)) | 2
out int | Total interest | $ | pmt * yrs * 12 - p | 2