Mortgage Calculator

How mortgage payments work

A mortgage payment covers both principal (the amount borrowed) and interest (the cost of borrowing). Early payments are mostly interest; later payments are mostly principal.

Formula

The monthly payment formula:

$$M = P \times \frac{r(1+r)^n}{(1+r)^n - 1}$$

Where:

• M = Monthly payment
• P = Principal (loan amount)
• r = Monthly interest rate (annual rate ÷ 12)
• n = Total number of payments

Example calculation

For a $320,000 loan at 6.5% for 30 years:

• Monthly rate: 0.065 ÷ 12 = 0.00542
• Number of payments: 30 × 12 = 360

$$M = \$320,000 \times \frac{0.00542(1.00542)^{360}}{(1.00542)^{360} - 1} = \$2,022$$

Loan term comparison

For a $320,000 loan at 6.5%:

Term	Monthly Payment	Total Interest
15 years	$2,789	$182,016
20 years	$2,389	$253,360
30 years	$2,022	$407,920

Shorter terms mean higher payments but significant interest savings.

Down payment

The amount you pay upfront affects your loan:

Benefits of larger down payment

• Lower loan amount = lower monthly payment
• Avoid Private Mortgage Insurance (PMI) at 20%+
• Better interest rates
• More equity from day one

Common down payment amounts

Percentage	On $400,000 home
3%	$12,000
5%	$20,000
10%	$40,000
20%	$80,000

Private mortgage insurance (PMI)

PMI protects the lender if you default on your loan. It's required when your down payment is less than 20%.

PMI costs

• Typically 0.5% to 1% of the loan amount annually
• On a $320,000 loan:$133-$267/month
• Adds up to $1,600-$3,200/year

Removing PMI

You can request PMI removal when:

• Your loan balance reaches 80% of the original home value
• Automatically removed at 78% loan-to-value
• Or through refinancing when you have 20%+ equity

Strategies to avoid PMI

1. Save for 20% down — The simplest approach
2. Piggyback loan (80-10-10) — 80% first mortgage, 10% second mortgage, 10% down
3. Lender-paid PMI — Higher interest rate but no separate PMI payment
4. VA or USDA loans — No PMI required for eligible borrowers

Total cost of ownership

Your monthly payment is just part of the cost:

PITI breakdown

• Principal
• Interest
• Taxes (property tax)
• Insurance (homeowner's)

Additional costs

• HOA fees
• Maintenance (budget 1-2% of home value/year)
• Utilities
• PMI (if down payment < 20%)

Interest rate impact

Small rate differences add up over 30 years:

$320,000 loan, 30-year term:

Rate	Monthly Payment	Total Interest
5.5%	$1,817	$334,120
6.0%	$1,919	$370,840
6.5%	$2,022	$407,920
7.0%	$2,129	$446,440

Each 0.5% increase costs ~$100/month and ~$35,000 over the life of the loan.

Fixed vs. adjustable rates

Fixed-rate mortgage

• Same rate for entire loan term
• Predictable payments
• Protection from rate increases
• Usually higher initial rate

Adjustable-rate mortgage (ARM)

• Lower initial rate (teaser rate)
• Rate adjusts after initial period (e.g., 5/1, 7/1)
• Payments can increase significantly
• May be good if planning to move/refinance

Amortization

Early payments are mostly interest:

Year 1 of a $320,000 loan at 6.5%:

• Monthly payment: $2,022
• Interest portion: ~$1,733
• Principal portion: ~$289

By year 25:

• Interest portion: ~$435
• Principal portion: ~$1,587

Prepayment strategies

Paying extra reduces total interest:

Extra monthly payment

Adding $200/month to a $2,022 payment on a $320,000 loan:

• Pay off 5+ years early
• Save ~$80,000 in interest

Bi-weekly payments

Paying half monthly payment every 2 weeks = 13 full payments/year instead of 12.

When to refinance

Consider refinancing when:

• Rates drop 0.5-1% below your current rate
• You plan to stay long enough to recoup closing costs
• You want to switch from ARM to fixed
• You need to remove PMI

Calculate break-even: Closing costs ÷ Monthly savings = Months to break even

How much house can you afford?

Lenders use several ratios to determine affordability:

The 28/36 rule

• Front-end ratio (28%): Housing costs shouldn't exceed 28% of gross monthly income
• Back-end ratio (36%): Total debt payments shouldn't exceed 36% of gross income

Example calculation

If your household income is $100,000/year ($8,333/month):

• Maximum housing payment: $8,333 × 28% = $2,333/month
• Maximum total debt: $8,333 × 36% = $3,000/month

Factors that affect approval

1. Credit score — Higher scores get better rates

   • 760+: Best rates
   • 700-759: Good rates
   • 620-699: Higher rates, may require larger down payment
   • Below 620: May need FHA loan or other options

2. Debt-to-income ratio (DTI) — Lower is better

   • Include car payments, student loans, credit cards
   • Most lenders want DTI below 43%

3. Employment history — Stable income preferred

   • 2+ years at same employer or in same field
   • Self-employed may need 2 years of tax returns

4. Cash reserves — Money left after closing

   • Lenders may require 2-6 months of payments in savings

Closing costs

Budget 2-5% of the home price for closing costs:

Cost	Typical range
Loan origination	0.5-1% of loan
Appraisal	$300-$500
Title insurance	$500-$3,500
Home inspection	$300-$500
Attorney fees	$500-$1,500
Recording fees	$100-$250
Prepaid taxes/insurance	Varies

On a $400,000 home, expect $8,000-$20,000 in closing costs.

Tips for getting the best rate

1. Improve your credit score — Pay down debt, fix errors on credit report
2. Shop multiple lenders — Rates vary significantly between lenders
3. Consider points — Paying points upfront can lower your rate
4. Lock your rate — Once you find a good rate, lock it in
5. Choose the right loan term — 15-year loans have lower rates than 30-year
6. Make a larger down payment — 20%+ often gets better rates