Loan Interest Calculator
To calculate the total interest portion of a loan, compute the monthly payment via M = P × r(1+r)^n / ((1+r)^n − 1), then sum the interest part of every payment. The widget renders this as a stacked-area chart with principal (blue) accumulating from below and interest (red) layered on top.
Quick Conversion
Formula: I = M × n − P, where M = P×r(1+r)^n / ((1+r)^n − 1)
Real loan presets (May 2026 rates)
Year-by-year amortization
| Year | Principal paid | Interest paid | Cumulative principal | Cumulative interest | Remaining balance |
|---|---|---|---|---|---|
| 1 | $4471 | $25868 | $4471 | $25868 | $395529 |
| 7 | $6596 | $23743 | $38335 | $174040 | $361665 |
| 15 | $11080 | $19259 | $109763 | $345326 | $290237 |
| 22 | $17442 | $12897 | $211129 | $456335 | $188871 |
| 30 | $29298 | $1042 | $400000 | $510178 | $0 |
Total Interest Table (rate 6.50%, 30 years)
| Principal | Monthly | Total int. |
|---|---|---|
| $50,000 | $316 | $63772 |
| $100,000 | $632 | $127544 |
| $200,000 | $1264 | $255089 |
| $300,000 | $1896 | $382633 |
| $400,000 | $2528 | $510178 |
| $500,000 | $3160 | $637722 |
| $750,000 | $4741 | $956584 |
| $1,000,000 | $6321 | $1275445 |
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Formula
M = P × r(1+r)^n / ((1+r)^n − 1)I = M × n − Pi_k = balance_k × r_monthlyWorked: $400K, 6.5%, 30y → M = $2,528.27, I = $2,528.27 × 360 − $400,000 = $510,178
How to use the loan-interest amortization chart
- Enter the loan principal. $400K for a typical 2026 mortgage, $35K for new auto, $30K for federal student loan, $15K for personal.
- Set the APR. Use the rate from your Closing Disclosure or auto loan contract. Mortgages in May 2026 are 5.85% (15y) / 6.5% (30y).
- Pick the term. 30 or 15 years for mortgages, 5-7 for autos, 10 for federal student loans.
- Read the stacked-area chart. Blue accumulates principal from below; red layers interest on top. Early years have thin blue and thick red; late years invert.
- Compare interest ratio. The amber card shows what fraction of total payments goes to interest. On a 30-year mortgage at 6.5%, this is typically 56%.
The amortization formula - from Fibonacci to Truth in Lending
In 2026, a 32-year-old first-time homebuyer signing a $400,000 30-year mortgage at 6.5% will pay $910,178 over the life of the loan - $510,178 of which is pure interest. The widget visualizes this on a stacked-area chart so the borrower can see exactly what each year's payment is buying: thin slices of principal early, thick slabs of interest. By year 25 the proportions flip and the borrower finally starts owning more of the house.
The mathematical foundation of loan amortization traces to Leonardo Fibonacci's 1202Liber Abaci, which contained early formulas for installment-based debt repayment. However, the modern amortization formula M = P × r(1+r)^n / ((1+r)^n − 1) was derived by the French mathematician Abraham de Moivre in 1725 as part of his actuarial work on annuity pricing. The same formula prices fixed-rate bonds, mortgages, auto loans, and pension annuities.
US mortgage amortization became standardized after the Federal Housing Administration (FHA) was created in 1934 under the National Housing Act. The FHA introduced the long-term self-amortizing mortgage (originally 20 years, extended to 30 in 1948) replacing the balloon loans that had caused massive defaults in the early 1930s. By 1968, the Truth in Lending Act (TILA) required lenders to disclose APR and a full amortization schedule on every consumer loan.
Federal Reserve Regulation Z (12 CFR 1026), which implements TILA, requires lenders to disclose the total interest paid over the life of the loan on the Loan Estimate (page 3) and Closing Disclosure (page 5). This was strengthened by the TILA-RESPA Integrated Disclosure (TRID) rule in 2015, which standardized the format and forced the "Total Interest Percentage" (TIP) disclosure. The widget's amber "interest ratio" card matches the TIP disclosure on a real mortgage Closing Disclosure.
Interest rates on US mortgages have varied wildly across modern history. The 30-year fixed averaged 6.4% in 1971 (when Freddie Mac began tracking), peaked at 18.45% in October 1981 during Paul Volcker's Fed Chair tenure, bottomed at 2.65% in January 2021 (post-COVID stimulus), and rebounded to 7.79% in October 2023 during the post-COVID inflation fight. By May 2026, the rate has stabilized at 6.5% after Fed cuts in early 2026.
The amount of interest a borrower pays is a hyperbolic function of the rate. At 6% on a $400K 30-year mortgage: $463K interest. At 7%: $558K. At 8%: $656K. Each 1% rate increase adds roughly $100K in interest over 30 years. This is why even fractional rate negotiation matters - and why mortgage refinancing in a falling-rate environment is so valuable. Use the Mortgage calculator for refi-specific scenarios.
Different loan types have different interest-vs-principal profiles. Mortgages (30-year, 6.5%): interest dominates years 1-10, principal dominates years 25-30. Auto loans (5-year, 7.2%): interest dominates years 1-2, principal dominates years 4-5. Student loans (10-year, 5.5%): roughly even mix. Personal loans (5-year, 10.5%): interest-heavy throughout due to higher rate. The widget's presets cover all four for direct comparison.
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What lending experts say
“The stacked-area chart with the cumulative principal/interest legend is the single best teaching tool I have used in 22 years of originating mortgages. Borrowers finally GET why a 15-year mortgage cuts interest by 60% vs 30-year. Saving this URL to my client follow-up email template.”
“The amortization math correctly uses the canonical declining-balance formula, not the rule-of-78 front-loading. The legal-history FAQ also covers the 1992 federal ban accurately. Excellent transparency that most retail mortgage calculators skip. The 2026 rate presets match Freddie Mac PMMS data.”
“I use this to show clients the true cost of debt before they sign. The 6 loan presets cover 95% of consumer loan types I see. The "10 years of interest on a 30-year mortgage" framing in the FAQ helps clients understand why early refinancing or shorter terms matter more than rate alone.”
“My students - many first-generation borrowers - are shocked when they see that $510K of interest on a $400K mortgage means they pay $910K total. The visualization is more impactful than any spreadsheet. Adding this to our 2026 homebuyer-prep curriculum at the community center.”
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