Loan Amortization Calculator
Free Loan amortization Calculator for financial & business math. Enter values to get step-by-step solutions with formulas and graphs.
Formula
M = P x r(1+r)^n / ((1+r)^n - 1)
Where M = monthly payment, P = principal loan amount, r = monthly interest rate (annual rate / 12), and n = total number of payments. Each payment splits between interest (balance x rate) and principal (payment minus interest). Extra payments reduce principal directly, saving future interest.
Worked Examples
Example 1: Standard 30-Year Mortgage
Problem: Calculate the monthly payment and total interest on a $300,000 mortgage at 6% for 30 years.
Solution: Monthly rate r = 0.06/12 = 0.005, periods n = 360\nM = 300,000 x 0.005(1.005)^360 / ((1.005)^360 - 1)\nM = 300,000 x 0.005 x 6.02258 / (6.02258 - 1)\nM = 300,000 x 0.030113 / 5.02258\nM = $1,798.65 per month\nTotal paid = $1,798.65 x 360 = $647,515\nTotal interest = $647,515 - $300,000 = $347,515
Result: Monthly Payment: $1,799 | Total Interest: $347,515 | Total Paid: $647,515
Example 2: Impact of Extra $200/Month
Problem: Same $300,000 loan at 6% for 30 years, but adding $200/month extra toward principal.
Solution: Base monthly payment: $1,798.65\nWith $200 extra: $1,998.65/month\nThe extra $200 goes entirely to principal each month\nNew payoff time: approximately 303 months (25.25 years)\nTotal interest with extra payments: $282,744\nInterest saved: $347,515 - $282,744 = $64,771\nMonths saved: 360 - 303 = 57 months (4.75 years)
Result: Saves $64,771 in interest | Pays off 4.75 years early | 57 fewer payments
Frequently Asked Questions
How is the monthly payment on an amortized loan calculated?
The monthly payment is calculated using the formula M = P x r(1+r)^n / ((1+r)^n - 1), where P is the principal loan amount, r is the monthly interest rate (annual rate divided by 12), and n is the total number of monthly payments. This formula ensures that each equal payment covers the interest due and progressively pays down principal so the loan reaches zero at the end of the term. For a $250,000 loan at 6.5% over 30 years, the monthly payment would be $1,580. The formula comes from setting the present value of all future payments equal to the initial loan amount.
How do extra payments affect my loan payoff?
Extra payments go entirely toward reducing the principal balance, which has a powerful compounding effect. By lowering the principal faster, you reduce the interest charged in every subsequent month, creating a snowball effect. Even an extra $100 per month on a $250,000 mortgage at 6.5% can save you over $50,000 in interest and shave nearly 5 years off a 30-year loan. The key is that extra payments eliminate future interest that would have been charged on that principal amount for the remaining life of the loan. Making extra payments early in the loan term has the greatest impact because there are more remaining years for the savings to compound.
What happens to the interest-to-principal ratio over the life of a loan?
The interest-to-principal ratio shifts dramatically throughout the loan term, following a pattern that surprises many borrowers. In the first year of a 30-year mortgage at 6%, approximately 80% of each payment goes to interest and only 20% to principal. By the halfway point around year 15, the split is roughly 50/50. In the final years, nearly all of each payment goes to principal. This front-loading of interest is why refinancing after many years of payments may not save as much as expected, since you would restart the amortization schedule. It also explains why extra payments in the early years have the most dramatic effect on total interest savings.
How does an amortization schedule help with financial planning?
An amortization schedule provides a complete roadmap of your loan, showing exactly how much goes to principal and interest each month for the entire loan term. This transparency enables several planning strategies. You can see how much equity you will have at any future point, which is important for home equity loans or selling decisions. You can calculate the impact of extra payments before committing to them. Tax planners use the schedule to project mortgage interest deductions for future years. It also helps compare different loan options side by side, revealing the true cost differences that are not apparent from just looking at monthly payments.
What is negative amortization and when does it occur?
Negative amortization occurs when monthly payments are insufficient to cover the interest due, causing the unpaid interest to be added to the loan balance. This means you actually owe more over time instead of less. It commonly happens with certain adjustable-rate mortgages (ARMs) that offer artificially low initial payments, payment-option loans, or income-driven student loan repayment plans. For example, if interest due is $1,500 per month but the minimum payment is only $1,200, then $300 gets added to your balance each month. Negative amortization is generally considered risky because borrowers can end up owing significantly more than their property is worth, especially in declining markets.
How do adjustable-rate mortgages affect amortization?
Adjustable-rate mortgages (ARMs) complicate amortization because the interest rate changes at predetermined intervals after an initial fixed-rate period. When rates adjust, the payment amount is recalculated based on the remaining balance, new rate, and remaining term. If rates increase, payments go up and a larger portion goes to interest, slowing principal paydown. If rates decrease, payments may drop and more goes to principal. Most ARMs have caps limiting how much the rate can increase per adjustment period and over the loan lifetime. When analyzing ARM amortization, it is crucial to model different rate scenarios to understand the range of possible outcomes and plan accordingly.