How to use this calculator
- Enter or choose future lump sum.
- Enter or choose regular payment per period.
- Enter or choose discount rate (per year).
- Enter or choose years.
- Enter or choose periods per year.
- The present value updates as you type. Use Copy result or Share to keep it.
Method
PV = FV ÷ (1 + i)ⁿ + PMT × (1 − (1 + i)^−n) ÷ i × (1 + i if paid at the start)
- i
- annual rate ÷ periods per year
- n
- years × periods per year
- PMT
- payment each period
Worked example
- (1.05)¹⁰ = 1.628895.
- PV = 10,000 ÷ 1.628895 = $6,139.13.
$10,000 received in 10 years is worth $6,139.13 today at a 5% discount rate.
What the result means
Use a discount rate equal to the return you could earn elsewhere with similar risk. A higher rate or a longer wait makes future money worth less today.
Assumptions and limits
- A constant rate, compounded once per payment period.
- Payments are equal and evenly spaced.
- Growing payments and irregular dates are not modelled.
Questions
What discount rate should I use?
The return you give up by waiting: for personal decisions, a savings or investment rate; for a business, its cost of capital.
What does “start of period” change?
Each payment arrives one period earlier, so it is discounted one period less and the PV is higher by a factor of (1 + i).