Loan Calculator
| Year | Principal Paid | Interest Paid | Ending Balance |
|---|---|---|---|
| 1 | $3,425.26 | $1,383.85 | $16,574.74 |
| 2 | $3,691.17 | $1,117.93 | $12,883.56 |
| 3 | $3,977.73 | $831.38 | $8,905.84 |
| 4 | $4,286.53 | $522.58 | $4,619.31 |
| 5 | $4,619.31 | $189.80 | $0.00 |
How Loan Payments Are Calculated
Every fixed-rate loan uses the same underlying math: each month, interest accrues on the outstanding balance, and your payment covers that interest first before reducing the principal. Because the balance shrinks with each payment, the interest portion of each installment declines while the principal portion grows — even though your monthly payment stays the same. This mechanism is called amortization, from the Latin for "killing off" the debt gradually.
The precise monthly payment is determined by three variables: the loan amount (principal), the annual interest rate, and the repayment term in months. The formula produces a constant payment that exactly zeros out the balance on the final payment date — no rounding surprises, no balloon payment.
The Loan Payment Formula
The standard amortizing loan payment formula is:
M = P × [r(1+r)n] / [(1+r)n − 1]
| Variable | Meaning | Example |
|---|---|---|
| M | Monthly payment | $400.76 |
| P | Principal (loan amount) | $20,000 |
| r | Monthly interest rate (annual rate ÷ 12) | 0.625% = 0.00625 |
| n | Total number of monthly payments | 60 (5 years) |
Worked Example — Step by Step
Calculate the monthly payment on a $20,000 loan at 7.5% annual interest for 5 years (60 months):
How Loan Term Affects Cost
The single most powerful lever in reducing total interest paid is the loan term. Shorter terms mean higher monthly payments, but the loan balance shrinks faster — reducing the balance on which interest accrues. The table below shows how dramatically the term affects cost on the same $20,000 loan at 7.5%:
| Loan Term | Monthly Payment | Total Paid | Total Interest | Interest % of Loan |
|---|---|---|---|---|
| 1 year (12 mo) | $1,732.81 | $20,793.72 | $793.72 | 3.97% |
| 2 years (24 mo) | $898.52 | $21,564.48 | $1,564.48 | 7.82% |
| 3 years (36 mo) | $621.97 | $22,390.92 | $2,390.92 | 11.95% |
| 5 years (60 mo) | $400.76 | $24,045.60 | $4,045.60 | 20.23% |
| 7 years (84 mo) | $303.73 | $25,513.32 | $5,513.32 | 27.57% |
Stretching from a 3-year to a 7-year term saves $318.24 per month but costs an additional $3,122.40 in interest over the life of the loan — equivalent to more than 10 months of the monthly savings you gained. Every borrower must weigh cash flow needs today against total cost over time.
How Interest Rate Affects Your Payment
The interest rate directly determines the interest charge on every outstanding dollar. Even a 1% difference in rate is meaningful over a multi-year term. The table below shows the impact of rate on a $20,000 5-year loan:
| Interest Rate | Monthly Payment | Total Interest | vs. 5% Rate |
|---|---|---|---|
| 5.0% | $377.42 | $2,645.20 | — |
| 6.0% | $386.66 | $3,199.60 | +$554.40 |
| 7.5% | $400.76 | $4,045.60 | +$1,400.40 |
| 10.0% | $424.94 | $5,496.40 | +$2,851.20 |
| 15.0% | $475.80 | $8,547.80 | +$5,902.60 |
| 20.0% | $529.88 | $11,792.80 | +$9,147.60 |
A borrower who improves their credit score from fair to good — dropping their rate from 15% to 7.5% — saves $4,501.90 in interest on a $20,000 5-year loan. Shopping multiple lenders for even a half-point better rate can save hundreds of dollars.
Understanding Amortization
Amortization refers to the process of paying off a loan through regular scheduled payments. Although the monthly payment stays constant, its composition shifts over time. In the early months, interest consumes the majority of each payment because the outstanding balance is at its highest. As payments are made and the balance falls, less interest accrues, and more of each fixed payment attacks the principal.
On a $20,000 loan at 7.5% for 5 years, the first payment of $400.76 breaks down as: $125.00 interest (7.5% / 12 × $20,000) and $275.76 principal. By the last payment, the balance is just over $400, so nearly the entire payment is principal — only about $2.50 is interest.
This front-loading of interest means that paying off a loan early delivers outsized savings. Paying off the $20,000 loan at month 30 (halfway through) does not save half the interest — it saves far more than half, because all the remaining interest would have been charged on a declining balance that never got to shrink.
Types of Loans That Use This Calculator
This calculator applies to any fixed-rate installment loan where payments are equal each month and the loan is fully paid off at the end of the term. Common examples include:
- Personal loans — unsecured loans from banks, credit unions, or online lenders. Rates typically 6-36% depending on credit.
- Auto loans — secured by the vehicle. Rates typically 4-15% for new cars. Terms usually 24-84 months.
- Student loans — federal rates set annually by Congress; private rates vary widely.
- Home improvement loans — personal loans used for renovation. Faster and simpler than HELOCs for smaller projects.
- Debt consolidation loans — used to replace multiple high-rate debts with a single lower-rate payment.
Mortgages use the same formula but typically have more complex total cost calculations involving property tax, insurance, and possibly PMI. Use the Mortgage Calculator for home purchase scenarios.
Frequently Asked Questions
What is the formula for calculating a monthly loan payment?
The standard loan payment 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. For a $20,000 loan at 7.5% for 5 years: r = 0.075/12 = 0.00625, n = 60, giving a monthly payment of $400.76.
How does the loan term affect the monthly payment and total interest paid?
A longer loan term lowers the monthly payment but increases the total interest paid. On a $20,000 loan at 7.5%: a 3-year term costs $621.97/month and $2,390.84 in interest; a 5-year term costs $400.76/month but $4,045.52 in interest; a 7-year term costs $303.73/month but $5,512.98 in interest. Choose the shortest term your budget allows to minimize interest costs.
What is an amortization schedule?
An amortization schedule is a complete table of loan payments broken down month-by-month into principal and interest components. In the early months of a loan, the majority of each payment covers interest because the balance is high. As the balance falls, more of each payment goes toward principal. By the final payment, nearly all of it is principal. This front-loading of interest is why paying off a loan early saves disproportionately more interest.
Does making extra payments reduce my loan faster?
Yes — significantly. Any extra payment applied to principal reduces the balance immediately and cuts the interest charged on every subsequent payment. On a $20,000 loan at 7.5% for 5 years, paying an extra $50/month shortens the loan by about 6 months and saves roughly $300 in interest. Extra payments work best early in the loan when the outstanding balance (and therefore the interest charge) is highest.
What credit score do I need to get a good loan interest rate?
Lenders typically tier rates by credit score. Excellent credit (750+) qualifies for the best rates, often 2-4% below the average. Good credit (700-749) gets near-prime rates. Fair credit (640-699) sees rates 3-6% higher than top tier. Poor credit (below 640) may face rates 8-15% above prime or outright denial. Even a 2% rate difference on a $20,000 5-year loan costs an extra $1,050 in interest — worth checking your credit report before applying.
Related Calculators
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- Debt Payoff Calculator — Snowball vs. avalanche payoff strategies
- Compound Interest Calculator — Future value of savings and investments