How to use this calculator
- Enter or choose n (number of periods).
- Enter or choose i/Y (annual interest rate).
- Enter or choose pV (present value).
- Enter or choose pMT (payment per period).
- Enter or choose fV (future value).
- The solved value updates as you type. Use Copy result or Share to keep it.
Method
PV(1+i)^N + PMT(1 + i·t)((1+i)^N − 1)/i + FV = 0, with i = I/Y ÷ periods per year and t = 1 for payments at the beginning, 0 at the end. I/Y is found numerically.
- N
- number of periods
- i
- interest rate per period
- PV, PMT, FV
- cash flows: positive when received, negative when paid
Worked example
- i = 6% ÷ 12 = 0.5% per period; (1.005)^360 = 6.022575.
- PMT = −(FV + PV × 6.022575) ÷ ((6.022575 − 1) ÷ 0.005) = −602,257.52 ÷ 1,004.515 = −599.55.
Borrowing 100,000 (received, positive) at 6% over 360 months means paying 599.55 a month (negative).
What the result means
Signs carry meaning: a loan is a positive PV (cash in) with negative payments (cash out); a savings plan is negative deposits that build a positive FV. If no answer exists, check that the signs make sense.
Assumptions and limits
- Interest compounds once per period, at the same rate throughout.
- All payments are equal and evenly spaced.
- For irregular cash flows use an NPV or IRR method instead.
Questions
Why is my payment negative?
It is money you pay out. Financial calculators use a sign convention so that the five values balance to zero.
Is this the same as a BA II Plus or HP 12C?
It uses the same equation, with periods per year acting like P/Y = C/Y on those calculators.
Please note: This calculator gives estimates for planning. It is not financial advice, and lenders’ actual terms, fees and rounding may differ.