Quick answer: A 200,000 loan (PV = 200,000) at I/Y = 6% with N = 360 monthly payments and FV = 0 gives PMT = −1,199.10 a month.
How it's calculated
All five values are tied by one equation: PV(1 + i)^N + PMT(1 + i·t)((1 + i)^N − 1)/i + FV = 0, where i = I/Y ÷ P/Y is the rate per payment period and t = 1 for payments at the beginning of each period (BGN) or 0 at the end (END).
Signs show the direction of money. Money you receive is positive and money you pay out is negative: for a loan you receive PV (+) and pay PMT (−); for savings you pay PV and PMT (−) and receive FV (+). If the signs are all the same, there is no answer.
PV, PMT and FV are solved directly; N with logarithms; I/Y numerically, the same way as the RATE function. For a plain loan payment the loan calculator is simpler, and the interest rate calculator finds a loan's rate.
Worked examples
- Loan: N 360, I/Y 6, PV 200,000, FV 0: PMT = −1,199.10
- Saving: N 120, I/Y 6, PV −500, PMT −200 (BGN): FV = 33,849.45
- N 48, PV 8,000, PMT −200, FV 0: I/Y = 9.2418%
Frequently asked questions
Why is my payment negative?
It is money you pay out. The calculator follows the sign convention of financial calculators and spreadsheets.
What is P/Y?
Payments per year: 12 for monthly, 4 for quarterly, 1 for yearly. I/Y is always entered as a yearly rate and is divided by P/Y.
Why do I get no answer?
Usually the signs: if PV, PMT and FV all have the same sign, no rate or number of periods can balance the equation.
BGN or END?
END for loans and most savings plans (the payment is made at the end of each period). BGN for rent, leases and annuities due.
What does I/Y mean?
The interest rate per year, as a percentage. Enter 6 for 6%, not 0.06.
How do I enter a savings plan?
Money you pay out is negative. For saving 500 a month, enter PMT as −500 and solve for FV, which comes out positive.