How it works

A useful distinction

Discount by division rather than subtraction

Receiving 1,000 in one year at a 10% discount rate is worth 909.09 today, not 900. Dividing by 1.10 reverses growth; subtracting 10% from the future amount uses the wrong base.

Choosing the discount rate and payment timing

Present value expresses future money as an equivalent amount at the selected discount rate. A future lump sum and a stream of payments require different inputs. Check the payment frequency and whether payments arrive at the start or end of a period. The discount rate is an assumption you supply; changing it can materially change the value assigned to the same future cash flows.

Present value: formula and assumptions

PV = FV/(1+r)^n + PMT[1−(1+r)^−n]/r.

Annual payments are assumed to occur at the end of each year.

Payment frequency and timing: formula and assumptions

PV=FV/(1+i)^n+PMT×[1−(1+i)^−n]/i, multiplied by (1+i) for beginning payments.

The annual rate is effective; the equivalent periodic rate is (1+r)^(1/periods)−1.

Worked example

Reference example currency: USD. These fixed examples do not change with your calculator preferences.

Using the Present value example:

Inputs

Future lump sum ($): 50000
Annual future payment ($): 0
Annual discount rate (%): 5
Years: 10

Method

PV = FV/(1+r)^n + PMT[1−(1+r)^−n]/r.

Result

Example result

Present value: $30,695.66

These are illustrative inputs. Change the values to explore a different scenario.

Formula references

References explain the underlying methods; they do not imply endorsement or individual professional review of Finflo.

Common questions

Why does a higher discount rate reduce present value?

Future payments are divided by larger growth factors, so their equivalent value today becomes smaller.

Are annual and monthly payments treated the same way?

No. The timing mode converts the effective annual rate to the selected payment interval and uses the corresponding number of periods.

Prepared by Finflo. See our methodology and editorial policy. Read the relevant professional-advice limitations.

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