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Whether you are comparing auto loan offers, planning a home purchase, or figuring out how fast you can pay off a personal loan, the math is the same. Every fixed-rate loan in existence uses the same formula. This guide explains that formula, shows you exactly how much common loans cost, and demonstrates how extra payments can save you tens of thousands of dollars.
Every fixed-rate loan payment is calculated with one formula:
M = P[r(1+r)n] / [(1+r)n - 1]
Here is a concrete example. You borrow $25,000 at 7% annual interest for 5 years:
Total paid over 5 years: $29,701.80. Total interest: $4,701.80. That means you pay 18.8% more than you borrowed — and that is on a relatively short, moderate-rate loan.
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When you compare loan offers, you will see two numbers: the interest rate and the APR. They are not the same thing, and confusing them can cost you money.
The interest rate is the pure cost of borrowing money — it is what you plug into the payment formula. A 7% interest rate on a $25,000 loan means you pay 7% per year on the outstanding balance.
The APR (Annual Percentage Rate) includes the interest rate plus all other loan fees rolled into a single annual number. Origination fees, closing costs, discount points, and certain insurance premiums all get factored in. A loan with a 6.5% interest rate and $3,000 in fees might have a 7.1% APR.
Use the interest rate when calculating monthly payments. Use APR when comparing two loan offers side by side — the higher APR tells you which loan actually costs more, even if it has a lower interest rate.
This is where loan math gets interesting. Extra payments go directly toward your principal balance, reducing the amount that accrues interest going forward. The savings compound over time.
Here is a real example with a $200,000 mortgage at 6.5% for 30 years:
| Scenario | Monthly Payment | Total Interest | Loan Term | Interest Saved |
|---|---|---|---|---|
| Standard payments | $1,264 | $255,088 | 30 years | — |
| Extra $100/month | $1,364 | $207,586 | 25.7 years | $47,502 |
| Extra $200/month | $1,464 | $172,720 | 22.3 years | $82,368 |
| Extra $500/month | $1,764 | $115,841 | 16.8 years | $139,247 |
| Biweekly (half payment every 2 weeks) | $632 biweekly | $206,090 | 25.5 years | $48,998 |
An extra $200 per month on a $200,000 mortgage saves you over $82,000 in interest and cuts 7.7 years off the loan. That is $200 per month turning into $82,000 in savings — a 34x return on the extra payments.
The payment formula works for any fixed-rate loan. Here is what changes between loan types:
Find your approximate monthly payment below. This table assumes a standard fixed-rate loan with no extra payments.
| Loan Amount | 5% / 5yr | 7% / 5yr | 5% / 15yr | 7% / 15yr | 6.5% / 30yr |
|---|---|---|---|---|---|
| $10,000 | $188.71 | $198.01 | $79.08 | $89.88 | $63.21 |
| $25,000 | $471.78 | $495.03 | $197.70 | $224.71 | $158.03 |
| $50,000 | $943.56 | $990.06 | $395.40 | $449.41 | $316.03 |
| $100,000 | $1,887.12 | $1,980.12 | $790.79 | $898.83 | $632.07 |
| $200,000 | $3,774.25 | $3,960.24 | $1,581.59 | $1,797.66 | $1,264.14 |
| $300,000 | $5,661.37 | $5,940.36 | $2,372.38 | $2,696.48 | $1,896.20 |
| $500,000 | $9,435.62 | $9,900.60 | $3,953.97 | $4,494.14 | $3,160.34 |
Our loan calculator handles the core math for any fixed-rate loan. But some situations need specialized tools:
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