How to use this calculator
- Enter or choose loan amount.
- Enter or choose interest rate (per year).
- Enter or choose loan term.
- Enter or choose payments.
- Enter or choose interest compounds.
- The payment per period updates as you type. Use Copy result or Share to keep it.
Method
i = (1 + r/m)^(m/p) − 1; Payment = L × i × (1 + i)^n ÷ ((1 + i)^n − 1); n = years × p
- L
- loan amount
- r
- nominal annual interest rate
- m
- compounding periods per year
- p
- payments per year
- i
- interest rate per payment period
- n
- number of payments
Worked example
- Monthly payments with monthly compounding: i = 6% ÷ 12 = 0.5% per month; n = 30 × 12 = 360.
- (1.005)^360 = 6.022575, so Payment = 100,000 × 0.005 × 6.022575 ÷ 5.022575 = $599.55.
- Total paid = 599.5505 × 360 = $215,838.19, of which $115,838.19 is interest.
A $100,000 loan at 6% over 30 years costs $599.55 a month and $115,838.19 in interest.
What the result means
The payment is fixed, but its make-up changes: early payments are mostly interest and later ones mostly principal (see the yearly summary). Paying more often at the same annual rate saves a little interest because the balance falls sooner.
Assumptions and limits
- The interest rate is fixed for the whole term.
- Every payment is made on time and in full; the last payment is adjusted for rounding.
- Fees, insurance and taxes are not included.
- Lenders may round the payment differently or quote an APR that includes fees, so their figure can differ by a few cents or more.
- Variable-rate, interest-only and balloon loans need a different calculation.
Questions
Why does semi-annual compounding give a lower payment?
Interest compounds less often, so the effective annual rate is lower: 6% compounded semi-annually is 6.09% a year, against 6.17% compounded monthly.
Is paying every two weeks the same as paying half the monthly amount?
Not quite. 26 half-payments equal 13 monthly payments a year, so an “accelerated biweekly” plan pays the loan off faster. This calculator gives the true biweekly payment that repays the loan over the term you enter.
What is the difference between the interest rate and the effective rate?
The interest rate is the nominal annual rate. The effective annual rate shows what it amounts to once compounding is included.
Please note: This calculator gives estimates for planning. It is not financial advice, and lenders’ actual terms, fees and rounding may differ.