Annuity Payment Calculator

Find the level payment that exhausts a principal over a set term.

How the Math Works

The Annuity Payment Calculator uses the formula PMT = PV × r ÷ (1 − (1+r)^-n) to determine the fixed periodic payment required for an annuity. Here, PMT represents the payment amount, PV is the present value (initial sum), r is the periodic interest rate, and n is the number of payment periods. The calculation accounts for the time value of money by discounting future payments, where the denominator adjusts for compound interest effects over the annuity's term, ensuring that the present value of all future payments equals the initial principal amount.

Practical Applications

To apply this calculation, first identify your initial investment amount (PV), determine the annual interest rate and convert it to a periodic rate (r) by dividing by the number of periods per year, then count the total number of payment periods (n). For example, if you're calculating monthly payments on a $50,000 loan over 5 years at 6% annual interest, you would use PV=50000, r=0.06/12=0.005, and n=5*12=60. Input these values into the formula or calculator to determine your fixed monthly payment amount.

Day-to-Day Use

This calculator helps in day-to-day financial planning by enabling you to evaluate loan options, compare different investment scenarios, or plan for retirement. Whether you're considering a mortgage, auto loan, or personal loan, you can quickly determine what monthly payment fits your budget. It also helps you understand how changing interest rates or loan terms affect your payments, allowing you to make informed decisions about major purchases, debt consolidation, or savings strategies that align with your financial goals.

Worked example

$100,000 at 5% over 10 yr → ~$12,950/yr.

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