Present Value Calculator
Present Value Calculator
What a sum due in the future is worth today at a discount rate you choose — and what a stream of equal payments is worth today, paid at the end or the start of each period.
Present value
$10,00,000 received in 10 years, discounted at 8% a year, compounded yearly
Present value of a sum and of an annuity
Annuity: PV = P × [1 − (1 + i)−n] ÷ i; annuity due: the same × (1 + i)
FV = PV × (1 + i)n
- F
- the future sum
- P
- the equal payment each period
- i
- the rate per period: annual rate ÷ periods a year ÷ 100
- n
- the number of periods: years × periods a year
Worked example
$10,00,000 received in 10 years, discounted at 8% a year, compounded yearly
Discount factor = 1 ÷ 1.0810 = 0.4632
PV = 10,00,000 × 0.4632 = $4,63,193
Check: 4,63,193 invested at 8% for 10 years grows back to $10,00,000
Present value of 10,00,000 due in 10 years
| Discount rate | Value today |
|---|---|
| 4% | $6,75,564 |
| 6% | $5,58,395 |
| 8% | $4,63,193 |
| 10% | $3,85,543 |
| 12% | $3,21,973 |
Why money later is worth less than money now
A rupee today can be invested and become more than a rupee later, so a rupee promised later is worth less than one in hand. Present value runs compound interest backwards: it finds the sum that, invested today at the discount rate, would grow into the future amount. $10,00,000 due in ten years is worth $4,63,193 today at 8% a year — invest that and it grows back to ten lakh. The chart shows how quickly that value falls the further away the money is.
The discount rate carries the judgement. Use the return you could earn elsewhere at similar risk to compare an offer of money later with money now; use expected inflation to express a future sum in today’s prices, as the inflation calculator does. The same formula compounded monthly gives a slightly lower value, $4,50,523 in the example, because interest compounds more often.
For a stream of equal payments — rent, an annuity, instalments you are owed — enter the payment. The page assumes one payment per compounding period. Timing matters: paid at the start of each period (an annuity due), every payment arrives a period sooner, so the stream is worth more. $10,000 a month for five years at 7% is worth $5,05,020 paid at month-end and $5,07,966 paid at the start. The future value line shows the same total grown to the end of the period, the reverse view that the compound interest calculator and the lumpsum calculator take. Real payments are rarely certain, so a riskier promise deserves a higher discount rate. This is arithmetic on the figures you enter, not financial advice.
Frequently asked questions
How do you calculate present value?
Divide the future sum by (1 + rate) to the power of the number of periods. $10,00,000 in 10 years at 8% is 10,00,000 ÷ 1.0810 = $4,63,193.
What discount rate should I use?
The return you could earn on money of similar risk, or inflation to see a sum in today’s prices. The answer is only as good as that choice, so try more than one rate.
What is the difference between an ordinary annuity and an annuity due?
An ordinary annuity pays at the end of each period, an annuity due at the start. The annuity due is worth (1 + i) times more: $5,07,966 against $5,05,020 for $10,000 a month over five years at 7%.
How is present value related to future value?
They are the same calculation in opposite directions: FV = PV × (1 + i)n.
Related calculators
References
- Brealey RA, Myers SC, Allen F. Principles of Corporate Finance. McGraw-Hill. Present value, discount factors, the present value of an annuity and of an annuity due.