Every loan has the same underlying math, even when it looks different on the paperwork. Interest is the cost of borrowing money, calculated against the unpaid principal over time. The complications come from how often interest accrues, how payments split between principal and interest, and what the lender chose to include in the APR.
Key Takeaways
- Interest accrues against the outstanding principal, not the original loan amount.
- Most consumer loans use monthly amortization: each payment pays interest first, then principal.
- Early payments are mostly interest; late payments are mostly principal.
- Daily interest accrual (common in mortgages and credit cards) calculates a daily rate against the current balance.
- Extra principal payments reduce future interest by shrinking the base that interest is calculated on.
The Core Mechanic
When a lender quotes a 7% rate on a $300,000 mortgage, that rate is annualized. To turn it into a monthly accrual, divide by 12:
Monthly rate = 7% / 12 = 0.5833%
For the first month, interest is calculated against the full principal:
Month 1 interest = $300,000 × 0.005833 = $1,750
If your monthly payment is $1,996, the remaining $246 goes to principal. The new balance is $299,754. Month 2's interest is calculated against the new, slightly smaller balance.
That is amortization. The payment stays constant, but the split between principal and interest shifts every month.
Amortization in Action
Here is what the first six months and last six months of a $300,000, 30-year, 7% mortgage look like:
| Month | Payment | Interest | Principal | Balance |
|---|---|---|---|---|
| 1 | $1,996 | $1,750 | $246 | $299,754 |
| 2 | $1,996 | $1,749 | $247 | $299,506 |
| 3 | $1,996 | $1,747 | $249 | $299,258 |
| 4 | $1,996 | $1,746 | $250 | $299,007 |
| 5 | $1,996 | $1,744 | $252 | $298,756 |
| 6 | $1,996 | $1,742 | $254 | $298,501 |
| ... | ... | ... | ... | ... |
| 355 | $1,996 | $69 | $1,927 | $9,933 |
| 356 | $1,996 | $58 | $1,938 | $7,995 |
| 357 | $1,996 | $47 | $1,950 | $6,045 |
| 358 | $1,996 | $35 | $1,961 | $4,084 |
| 359 | $1,996 | $24 | $1,972 | $2,112 |
| 360 | $1,996 | $12 | $1,984 | $0 |
Early in the loan, 88% of each payment is interest. By the end, 99% is principal. This is the classic "front-loaded" structure of amortized loans, and it is the reason refinancing or extra principal payments are most effective early in a loan's life.
Daily vs Monthly Accrual
Different loan products calculate interest on different cycles.
Monthly accrual. Standard for most fixed-rate personal loans and traditional mortgages. Interest is calculated once a month against the balance on the statement date.
Daily accrual. Common for mortgages with daily-interest provisions, most credit cards, and many home equity lines of credit. The daily rate is the annual rate divided by 365 (sometimes 360 for "banker's days"). Interest accumulates each day on the current balance.
Daily accrual matters in two cases:
- Payment timing. Paying a daily-accrual loan 5 days early reduces the interest charged that month, because the balance is smaller for those 5 days.
- Carrying a balance. On a credit card, today's balance generates today's interest, which is added to tomorrow's balance. That is daily compounding, and it is why high-APR cards are expensive.
The Loan Payment Formula
The standard formula for the monthly payment on an amortizing loan is:
M = P × [r(1 + r)^n] / [(1 + r)^n − 1]
Where:
- M = monthly payment
- P = principal (loan amount)
- r = monthly interest rate (annual rate / 12, as decimal)
- n = number of monthly payments
For the $300,000 mortgage at 7% over 30 years:
- P = 300,000
- r = 0.07 / 12 = 0.005833
- n = 360
M = 300,000 × [0.005833 × (1.005833)^360] / [(1.005833)^360 − 1] M = 300,000 × [0.005833 × 8.116] / [8.116 − 1] M = 300,000 × 0.04735 / 7.116 M ≈ $1,996
This formula is the engine behind every mortgage, auto loan, and amortized personal loan calculator.
Simple-Interest Loans
A small number of loan products (most notably some auto loans and short-term personal loans) use simple interest. Interest accrues based on actual days the balance is outstanding, with no interest-on-interest. The formulas:
Daily interest = Principal × (Annual Rate / 365) Period interest = Daily interest × Days in period
Pay early: less interest accrues. Pay late: more accrues. Each payment is applied first to outstanding interest, then to principal.
The distinction matters less than the rate itself, but on a simple-interest auto loan, the payoff math is cleaner: there is no penalty for paying off early beyond losing any prepayment-clause provisions in the contract.
What Affects Total Interest Paid
Five variables drive total interest cost over a loan:
- Rate. Single biggest lever. Each percentage point on a 30-year mortgage shifts total interest by tens of thousands.
- Loan term. Longer terms reduce monthly payment but balloon total interest. A 30-year mortgage costs roughly 50–70% more in total interest than a 15-year at the same rate.
- Principal. Larger loans accrue more total interest at the same rate.
- Payment frequency. Biweekly payments shave years off a long loan because you make an extra full payment per year and reduce the principal balance faster.
- Extra payments. Any payment beyond the scheduled amount applies directly to principal (with most lenders), accelerating payoff and reducing future interest.
Worked Example: The Cost of an Extra $200/month
Same $300,000 mortgage at 7% over 30 years. Standard payment: $1,996. Total interest over 30 years: $418,527.
Add $200/month extra to principal:
- Loan paid off in roughly 23 years instead of 30
- Total interest paid: about $311,000
- Savings: roughly $107,000 in interest, plus 7 years freed from the loan
That is the leverage of attacking principal early: the entire compounding effect runs in reverse when you shrink the base.
Common Mistakes
Assuming the monthly payment changes when rates change. On a fixed-rate loan, the payment is fixed. The split between principal and interest within the payment is what varies if rates were applied differently, but on a fixed-rate amortized loan, neither changes.
Thinking refinancing late in the loan saves money. Refinancing resets the amortization clock. Late-stage loans are mostly principal, so refinancing into a new 30-year often increases lifetime interest even at a lower rate.
Confusing the note rate with APR. APR includes fees; the note rate doesn't. Two loans with the same APR can have different note rates depending on fee structure.
Ignoring escrow. Mortgage payments often include taxes and insurance. The "P&I" (principal and interest) portion is what amortizes; the escrow portion is pass-through.
Misapplying extra payments. Some lenders apply extra funds to future scheduled payments rather than current principal. Confirm with the lender that extra payments reduce principal directly.
Practical Scenarios
Scenario 1: Choosing 15- vs 30-year mortgage. $400,000 at 6.5%. 30-year payment: $2,528, total interest: ~$510,000. 15-year payment: $3,484, total interest: ~$227,000. Higher monthly cost, dramatically lower lifetime cost.
Scenario 2: Refinance breakeven. Current loan: $250,000 balance, 7%, 28 years remaining. Refinance offer: 6%, $4,000 closing costs. Monthly savings: about $170. Breakeven: 4,000 / 170 ≈ 24 months. If you plan to stay longer, the refinance saves money.
Scenario 3: Auto loan with prepayment. $25,000 at 8% over 5 years. Standard payment: $507, total interest: $5,415. Adding $100/month: paid off in 4 years, total interest: ~$4,300. Savings: about $1,100.
FAQ
Does my interest rate change as I pay down the loan? On a fixed-rate loan, no. The rate is fixed for the life of the loan. What changes is the dollar amount of interest, because it is applied against a shrinking balance.
Why is my early mortgage payment mostly interest? Because the balance is largest at the beginning. With a $300,000 balance at 7%, the first month's interest is $1,750, most of the $1,996 payment. As principal shrinks, the interest portion shrinks too.
Can I save money by paying biweekly instead of monthly? Yes, slightly. Biweekly means 26 half-payments per year, equivalent to 13 monthly payments. The extra payment goes to principal and shaves several years off a 30-year mortgage.
Does paying extra principal lower my monthly payment? On most fixed-rate loans, no. It shortens the loan term instead. To lower the monthly payment, you would need to recast or refinance.
What is amortization? The process of paying down a loan over time through scheduled payments that include both principal and interest. The schedule front-loads interest and back-loads principal.
How is credit card interest different? Credit cards use daily compounding on the average daily balance, with no fixed amortization. Minimum payments often barely cover interest, which is why card balances can persist for years.
What is negative amortization? A loan structure where the payment is less than the accrued interest, so the balance grows over time. Rare today but historically common in certain adjustable-rate mortgages.
Related Tools
Build your own schedule with the Loan Calculator or Amortization Calculator. For mortgages specifically, the Mortgage Calculator handles escrow, taxes, and PMI. The Auto Loan Calculator is optimized for shorter terms and trade-in scenarios.
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Final Thoughts
Loan interest math looks intimidating because of the formula, but the mechanic is simple: interest accrues against unpaid principal, and your payment chips away at both. The faster you reduce principal, the less interest accrues, which is why early extra payments compound into significant savings. Use the amortization schedule as a planning tool: it tells you exactly where your money is going, month by month, for the life of the loan.