The equation behind every solve
With periodic rate i, n periods, payment PMT, present value PV and future value FV, the cash flows net to zero: PV + PMT × [1 − (1 + i)−n] ÷ i + FV × (1 + i)−n = 0 for an ordinary annuity. For an annuity due the payment term is multiplied by (1 + i). The calculator rearranges this directly for PV, FV, PMT and n, and uses a numeric search for the rate. These are the standard annuity formulas of any corporate finance or intermediate accounting text, and the same ones a financial calculator uses.
When to use it
Recompute a client's discounting by hand when a spreadsheet model is opaque: a lease liability, a note with an unusual payment pattern, the imputed interest on a long-term receivable. Set the rate to the discount rate the client used, solve PV, and compare. To back into the rate a client implicitly used, enter the PV, the payments and the FV and solve for the rate.
Limits
This handles level payments at regular intervals with compounding that matches the payment frequency. It does not handle irregular cash flows, rate changes, balloon schedules that differ from FV, or day-count conventions. Fractional periods use the same compounding formula, which can differ from a lender's partial-period convention. The balance table appears when the number of periods is a whole number.
Illustrative figures only. Check the result against your firm's methodology before relying on it.
Common questions
What does a time value of money calculator solve?
Five variables tie together: number of periods (N), rate per period (I/Y), present value (PV), payment (PMT) and future value (FV). Give it four and it solves the fifth. Payments are an annuity: equal amounts at equal intervals.
What is the difference between an ordinary annuity and an annuity due?
An ordinary annuity pays at the end of each period (most loans, bond coupons). An annuity due pays at the start (rent and leases paid in advance). Payments in advance earn or cost one more period of interest, so the present value of an annuity due is the ordinary annuity value × (1 + i).
Why are some inputs negative?
The calculator follows the financial-calculator sign convention: money you pay out is negative and money you receive is positive. A loan has a positive PV (you receive it) and negative payments. A savings plan has negative deposits and a positive FV.
How is the interest rate solved?
There is no algebraic solution when payments are involved, so the calculator searches numerically for the periodic rate at which present value, payments and future value net to zero, then multiplies by periods per year for the stated annual rate. It returns the lowest rate above -99% that works, and tells you when none exists.
Where do auditors use present value math?
Recomputing lease liabilities and right-of-use assets under ASC 842, notes and bonds under ASC 835-30, asset retirement obligations, long-term receivables, pension and deferred compensation obligations, and any ASC 820 income-approach fair value that discounts cash flows.
Runs in your browser. The figures you type are not sent to CORAA or stored. Check the result against your firm's methodology before relying on it.