Annuity Payment Calculator
Find the level payment for a loan or withdrawal plan, or the deposit needed to hit a savings goal.
Total paid: $133,224.60 · Total interest paid: $33,224.60.
An annuity payment is the level amount paid each period, found with PMT = PV · i ÷ (1 − (1 + i)^−N), where i is the periodic rate and N the number of payments. Draw $100,000 at a 6% annual rate over 10 years, paid monthly (i = 0.005, N = 120), and each payment is about $1,110.21.
What an annuity payment is
An annuity is a stream of equal payments made at regular intervals. There are two mirror-image questions. In the present-value case you have a lump sum today — a loan balance or a retirement pot — and want the fixed payment that draws it down to zero over the term, with interest charged on the shrinking balance. In the sinking-fund case you have a future target and want the deposit that, with compounding, grows to that goal. Both use the same periodic rate i = annual rate ÷ payments per year and the same payment count N = years × payments per year.
Ordinary-annuity payment from a present value; i is the periodic rate and N the total number of payments. When i = 0, PMT = PV ÷ N.
Worked example
Borrow $100,000 at a 6% annual rate, repaid monthly over 10 years.
- 1 Find the periodic rate. i = 6% ÷ 100 ÷ 12 = 0.005 per month.
- 2 Count the payments. N = 10 years × 12 = 120 monthly payments.
- 3 Compute the discount factor. (1 + i)^−N = 1.005^−120 ≈ 0.549633.
- 4 Apply the payment formula. PMT = 100,000 × 0.005 ÷ (1 − 0.549633) = 500 ÷ 0.450367 ≈ $1,110.21.
- 5 Check the totals. 120 × $1,110.21 ≈ $133,224.60 paid, so about $33,224.60 is interest.
Present value vs. sinking fund
The same tool answers two opposite questions — start from a lump sum today, or aim at a target later.
| Present value (draw down) | Sinking fund (build up) | |
|---|---|---|
| You know | A lump sum today (PV) | A target amount later (FV) |
| You solve for | Payment that repays it | Deposit that reaches it |
| Formula | PMT = PV · i ÷ (1 − (1 + i)^−N) | PMT = FV · i ÷ ((1 + i)^N − 1) |
| Typical use | Loan, mortgage, retirement withdrawal | College fund, down-payment savings |
| If i = 0 | PMT = PV ÷ N | PMT = FV ÷ N |
Ordinary annuity vs. annuity due
This calculator models an ordinary annuity, where each payment lands at the end of the period — the convention for most loans, mortgages, and bonds. An annuity due pays at the start of each period instead, as with rent or many insurance premiums. Because every payment then sits and earns for one extra period, an annuity-due payment is smaller by a factor of (1 + i): multiply the ordinary payment by 1 ÷ (1 + i) to convert. Keep your rate and term on the same basis — a monthly plan needs a monthly rate and a payment count in months, not years.