Understanding Mortgage Payments
A mortgage is a loan used to purchase real estate, typically repaid over 15 to 30 years. Each monthly payment consists of two parts: principal (reducing the loan balance) and interest (the cost of borrowing). Early in the loan, most of your payment goes to interest. Over time, a larger share goes toward principal. Understanding how mortgage payments are calculated helps you make informed decisions about home buying.
The Monthly Payment Formula
Where:
M = Monthly payment
P = Principal (loan amount)
r = Monthly interest rate (annual rate ÷ 12)
n = Total number of payments (years × 12)
Step-by-Step Example: 30-Year Mortgage
Home price: $350,000, Down payment: $70,000 (20%), Loan amount: $280,000, Interest rate: 6.5%:
- Monthly rate: r = 6.5% ÷ 12 = 0.065 ÷ 12 = 0.005417
- Number of payments: n = 30 × 12 = 360
- Numerator: 0.005417 × (1.005417)360 = 0.005417 × 6.9916 = 0.03788
- Denominator: (1.005417)360 - 1 = 6.9916 - 1 = 5.9916
- Monthly payment: $280,000 × (0.03788 ÷ 5.9916) = $280,000 × 0.006321 = $1,769.88
Total Cost of Your Mortgage
Your monthly payment of $1,769.88 over 360 months means you pay:
$1,769.88 × 360 = $637,156.80
Total Interest = Total Paid - Loan Amount
$637,156.80 - $280,000 = $357,156.80
On a $280,000 loan at 6.5% for 30 years, you pay more in interest ($357,157) than the original loan amount! This is why even small rate differences matter enormously.
How Interest Rates Affect Payments
Here is how the monthly payment and total interest change for a $300,000 loan over 30 years:
| Interest Rate | Monthly Payment | Total Interest | Total Paid |
|---|---|---|---|
| 4.0% | $1,432 | $215,609 | $515,609 |
| 5.0% | $1,610 | $279,767 | $579,767 |
| 6.0% | $1,799 | $347,515 | $647,515 |
| 6.5% | $1,896 | $382,633 | $682,633 |
| 7.0% | $1,996 | $418,527 | $718,527 |
| 8.0% | $2,201 | $492,480 | $792,480 |
30-Year vs 15-Year Mortgage
Comparing a $300,000 loan at 6.5%:
| Feature | 30-Year | 15-Year |
|---|---|---|
| Monthly Payment | $1,896 | $2,613 |
| Total Interest | $382,633 | $170,388 |
| Total Paid | $682,633 | $470,388 |
| Interest Savings | — | $212,245 |
A 15-year mortgage has higher monthly payments but saves you over $212,000 in interest compared to a 30-year loan at the same rate.
Understanding Amortization
Amortization shows how each payment is split between principal and interest. Here is a snapshot for the first and later years of a $280,000 loan at 6.5%:
| Payment | To Interest | To Principal | Remaining Balance |
|---|---|---|---|
| Month 1 | $1,517 | $253 | $279,747 |
| Month 60 (Year 5) | $1,436 | $334 | $263,401 |
| Month 180 (Year 15) | $1,149 | $621 | $211,471 |
| Month 300 (Year 25) | $600 | $1,170 | $109,291 |
| Month 360 (Year 30) | $10 | $1,760 | $0 |
Tips for Homebuyers
- Shop for the best rate: Even 0.25% less can save tens of thousands over the loan's life.
- Make extra payments: Paying just $100 extra per month can shave years off your mortgage.
- Consider the 28/36 rule: Housing costs should not exceed 28% of your gross income, and total debt should stay below 36%.
- Factor in all costs: Property tax, insurance, PMI, and maintenance add significantly to your monthly housing expense.
- Save for a larger down payment: Putting 20% down avoids PMI (Private Mortgage Insurance) and reduces your loan amount.
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