How Loan Payments Are Calculated
The standard amortization formula is:
M = P · r(1+r)^n / ((1+r)^n − 1)
Where:
- M = monthly payment
- P = loan principal (amount borrowed)
- r = monthly interest rate (annual rate ÷ 12)
- n = total payments (years × 12)
Zero-interest edge case: When the rate is 0%, the formula reduces to M = P ÷ n (simple equal division). This calculator handles this correctly.
Worked Example — $300,000 at 7% for 30 years
- P = $300,000
- r = 7% ÷ 12 = 0.5833% = 0.005833
- n = 30 × 12 = 360
- M = $300,000 × 0.005833 × (1.005833)^360 / ((1.005833)^360 − 1)
- M = $1,995.91/month
- Total paid: $718,527 | Total interest: $418,527
How to Read an Amortization Table
An amortization table breaks each payment into its principal and interest components. In the early months of a 30-year mortgage at 7%, roughly 83% of your payment is interest and only 17% reduces the principal. This ratio gradually inverts over the life of the loan.
Key insight: the total interest you pay is directly proportional to how long you carry the loan. Paying even $100–$200 extra per month early in the loan dramatically reduces both interest paid and time to payoff.
Should I Make Extra Mortgage Payments?
Extra payments go directly to principal, not interest. The math works strongly in your favor:
- $200/month extra on a $300k, 7%, 30yr loan → saves ~$81,000 in interest, pays off ~7 years early.
- $500/month extra → saves ~$150,000, pays off ~14 years early.
- One-time lump sums work especially well in the first 5–10 years when the principal balance is highest.
Compare the return: every dollar you put toward principal effectively "earns" your mortgage interest rate tax-free. At 7%, that beats most savings accounts and many bonds.
15-Year vs 30-Year Mortgage: The Real Cost
On a $300,000 loan at 7%:
- 30-year: $1,996/mo · Total interest: $418,527
- 15-year: $2,696/mo · Total interest: $185,254
- Difference: $700/mo more, but $233,273 less in total interest.
The 15-year wins decisively on total cost. Choose 30-year if the lower payment provides financial flexibility you genuinely need.
Frequently Asked Questions
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The formula is M = P · r(1+r)^n / ((1+r)^n − 1), where P is the principal, r is the monthly interest rate (annual rate ÷ 12), and n is the total number of monthly payments (years × 12). For a $300,000 loan at 7% for 30 years, the monthly payment is $1,995.91.
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An amortization table shows every monthly payment broken down into principal and interest. Early in the loan, most of each payment is interest. Over time the ratio shifts toward principal. The table also shows remaining balance after each payment.
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Significantly. For a $300,000, 7%, 30-year mortgage: paying $200/month extra saves approximately $81,000 in interest and cuts 7 years off the term. Use the Extra Payment section above to model your exact scenario.
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A 15-year mortgage has a higher monthly payment but costs roughly 55–60% less in total interest. On a $300,000 at 7%: 30-year total interest is $418,527; 15-year is $185,254. You pay $700 more per month but save $233,000 overall.
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At 0% interest, the monthly payment is simply the principal divided by the number of months. No interest accrues. Example: $12,000 at 0% for 1 year = $1,000/month, total cost = $12,000 (no interest).