How to Calculate Monthly Loan Payments: The Amortization Formula with Worked Examples

The monthly payment on a fixed-rate loan is calculated with one formula: Payment = P × [r(1+r)^n] / [(1+r)^n - 1] Where: P = principal (loan amount), r = monthly interest rate (annual rate ÷ 12), n = total number of payments (years × 12). Worked example — a $300,000 mortgage at 7% for 30 years: P = $300,000. Annual rate = 7%, so monthly rate r = 0.07 ÷ 12 = 0.005833. Number of payments n = 30 × 12 = 360. Plug in: Payment = $300,000 × [0.005833 × (1.005833)^360] / [(1.005833)^360 - 1]. (1.005833)^360 = 8.1165. Numerator: 0.005833 × 8.1165 = 0.04735. Denominator: 8.1165 - 1 = 7.1165. Payment = $300,000 × (0.04735 / 7.1165) = $300,000 × 0.006653 = $1,995.91 per month. That $1,995.91 is the total monthly payment of principal and interest. Over 360 payments, you pay $1,995.91 × 360 = $718,528 total — meaning you pay $418,528 in interest on a $300,000 loan. The interest is more than the principal. This is the math that makes people's jaws drop and is why understanding amortization matters. Snap a photo of any loan payment problem and FinanceIQ solves it step by step — showing the formula, the substitution, and the calculation with the answer. This content is for educational purposes only and does not constitute financial advice.

Here is the part that surprises everyone: early payments are almost entirely interest. On the $300,000 mortgage example, your first payment of $1,995.91 splits: $1,750 goes to interest and only $245.91 goes to principal. You owe $299,754.09 after your first payment — barely a dent. Why? Because interest is calculated on the remaining balance each month. With $300,000 outstanding, one month of interest at 7% annual = $300,000 × 0.07 / 12 = $1,750. The remaining $245.91 of your payment reduces the principal. Next month, interest is calculated on $299,754.09 — slightly less interest ($1,748.57), slightly more principal ($247.34). This pattern continues for 360 months. The crossover point — where more of each payment goes to principal than interest — does not occur until approximately month 215 of a 30-year mortgage at 7%. That means for the first 18 years, the majority of every payment is interest. This is why the total interest paid ($418K) exceeds the loan amount ($300K). This math also explains why refinancing or extra payments have the most impact early in the loan — when you reduce the principal balance by $10,000 in year 2, you avoid paying interest on that $10,000 for the remaining 28 years. The same $10,000 extra payment in year 25 saves much less because there are only 5 years of interest remaining. FinanceIQ builds complete amortization schedules from any loan parameters — showing the month-by-month breakdown of interest, principal, and remaining balance.

The formula is identical for any fixed-rate installment loan. Only the numbers change. Car loan example: $35,000 at 6.5% for 5 years. P = $35,000. r = 0.065 ÷ 12 = 0.005417. n = 60. Payment = $35,000 × [0.005417 × (1.005417)^60] / [(1.005417)^60 - 1]. (1.005417)^60 = 1.3829. Payment = $35,000 × (0.007493 / 0.3829) = $35,000 × 0.01957 = $684.96/month. Total paid: $684.96 × 60 = $41,098. Interest: $6,098. Student loan example: $45,000 at 5.5% for 10 years. P = $45,000. r = 0.055 ÷ 12 = 0.004583. n = 120. Payment = $45,000 × [0.004583 × (1.004583)^120] / [(1.004583)^120 - 1]. Payment = approximately $488.15/month. Total paid: $58,578. Interest: $13,578. The pattern across all three loan types: shorter terms and lower rates dramatically reduce total interest. The same $35,000 car loan at 6.5% costs $6,098 in interest over 5 years. Over 7 years: $8,745 in interest (44% more interest for 2 extra years of payments). This is why financial advisors say take the shortest term you can afford — the monthly payment is higher but the total cost is lower.

Extra payments go entirely to principal reduction — they skip the interest component because interest is already covered by your regular payment. This makes extra payments disproportionately powerful. On the $300,000 mortgage at 7% for 30 years ($1,995.91/month): adding $200/month extra reduces the loan term from 30 years to approximately 22.5 years and saves approximately $115,000 in total interest. You pay $200 more per month but save $115,000 over the life of the loan — a return of roughly 6.6:1 on every extra dollar. Adding $500/month extra: reduces the term to about 18 years and saves approximately $195,000 in interest. At $500/month extra for 18 years, you invest $108,000 in extra payments and save $195,000 — an 80% return. One extra payment per year (the 13th payment strategy): make one additional full payment per year, spread across 12 months ($1,995.91 ÷ 12 = $166.33 extra per month). This reduces a 30-year mortgage to approximately 25 years and saves roughly $85,000 in interest. This is the most popular extra payment strategy because the monthly increase ($166) is modest but the lifetime savings are substantial. The important caveat: extra payments only help if you do not have higher-interest debt. Paying an extra $200/month on a 7% mortgage while carrying $10,000 in credit card debt at 22% is mathematically wrong — the credit card interest is costing you 3x more per dollar of balance. Pay off high-interest debt first, then apply extra to the mortgage. FinanceIQ calculates exact extra payment savings for any loan — enter the original terms and your extra payment amount and it shows the new payoff date, total interest saved, and effective return on each extra dollar.