Loan Calculator
Compare equal-installment and equal-principal loans with monthly payment, total interest and a repayment schedule.
Equal installment (annuity)
Equal principal
| Period | Payment | Interest | Principal | Remaining balance |
|---|---|---|---|---|
| 1 | 3082.8537 | 1750 | 1332.8537 | 498667.15 |
| 2 | 3082.8537 | 1745.335 | 1337.5187 | 497329.63 |
| 3 | 3082.8537 | 1740.6537 | 1342.2 | 495987.43 |
| 4 | 3082.8537 | 1735.956 | 1346.8977 | 494640.53 |
| 5 | 3082.8537 | 1731.2419 | 1351.6118 | 493288.92 |
| 6 | 3082.8537 | 1726.5112 | 1356.3425 | 491932.58 |
| 7 | 3082.8537 | 1721.764 | 1361.0897 | 490571.49 |
| 8 | 3082.8537 | 1717.0002 | 1365.8535 | 489205.63 |
| 9 | 3082.8537 | 1712.2197 | 1370.634 | 487835 |
| 10 | 3082.8537 | 1707.4225 | 1375.4312 | 486459.57 |
| 11 | 3082.8537 | 1702.6085 | 1380.2452 | 485079.32 |
| 12 | 3082.8537 | 1697.7776 | 1385.076 | 483694.25 |
| 240 | 3082.8537 | 999.52034 | 2083.3333 | 0 |
What is it
Two classic ways to repay a loan. Equal installment (annuity): every month you pay the same amount — part interest, part principal — computed by the formula M = P·r(1+r)^n / ((1+r)^n − 1). Equal principal: the principal is split into n equal slices, and each month you also pay interest on what is still owed, so the payment starts high and shrinks over time. Enter the principal, the annual interest rate and the number of months, and compare both side by side.
Notes & fun facts
The annuity formula is elegant but looks scarier than it is: it exists so that, at a fixed interest rate, the sum of all your discounted payments equals the money you originally borrowed. Banks love it because the monthly amount never changes, which makes budgeting easy for households too.
Origin & history
The mathematics of annuities was developed in 17th-century Europe — Edmond Halley published a famous work on life annuities in 1693, building on early tables by Johannes de Witt (1671). Fixed monthly home loans as we know them became standard in the United States in the 1930s, when the Federal Housing Administration popularized the long-term self-amortizing mortgage.