Financial calculator

How to calculate it

PV × (1 + r)^N + PMT × (1 + r × type) × ((1 + r)^N − 1) / r + FV = 0

PV is present value, FV is future value, PMT is the regular payment, r is the rate per period as a decimal, and N is the number of periods. Payment type is 0 for the end of each period or 1 for the beginning. At a zero rate, the equation becomes PV + PMT × N + FV = 0.

Reference: Microsoft: FV function and cash-flow conventions.

Worked example

Start with PV = −1,000, add PMT = −100 at the end of each year, earn 6% per year, and use 10 periods. Future value is 3,108.93. Moving those payments to the beginning of each year increases future value to 3,188.01.

Assumptions and limits

• Money paid out is negative; money received is positive. For savings, the opening deposit and contributions are negative and the future balance is positive. For a loan, the borrowed amount is positive and repayments are negative.
• Rates are per period. For monthly payments with a nominal 6% annual rate compounded monthly, enter 0.5% and use the number of months. An effective annual rate needs a different conversion: monthly rate = (1 + annual rate)^(1/12) − 1.
• The payment and rate stay constant. Fees, taxes, irregular dates, and changing payments are excluded. Some combinations do not determine a unique rate or number of periods; the calculator explains when it cannot solve them.

Results use unrounded inputs and normally display two decimal places. Very small or large numbers may use scientific notation. Use consistent currency units; no currency conversion is applied.

Common questions