What present value means
A dollar today is worth more than a dollar in five years, because today’s dollar can earn interest in the meantime. Present value turns future money into today’s money at an interest rate you choose, often called the discount rate. It answers questions like: what is a pension of $1,000 a month worth today, how much do I need to invest now to have $50,000 in five years, or which offer is better, a lump sum or payments over time?
The calculator works with five values. Enter four, and it solves for the fifth: the present value (PV), the future value (FV), the payment per period (PMT), the interest rate and the time.
Present value formulas
These are the time value of money formulas from OpenStax Principles of Finance, with i the interest rate per period and n the number of periods.
With a lump sum and payments together, the calculator adds the two present values. A single amount: at 5% a year, $50,000 due in 5 years is worth $39,176.31 today. A stream of payments: $25,000 a year for 5 years at 8% is worth $99,817.75 if each payment comes at the end of the year, and $107,803.17 if each comes at the start, the annuity due. Both match the worked examples in section 8.2 on annuities.
Paid out or paid in
Choose Paid out when the payments come out of the balance: a pension, an annuity, retirement withdrawals or the payments that repay a loan. The present value is then what those payments, plus anything left at the end, are worth today. $1,000 a month for 20 years at 5% compounded monthly is worth $151,525.31 today. For a loan, enter the amount borrowed as the present value and solve for the payment: $32,000 over 36 months at 6% costs $973.50 a month, the same as the financial calculator example in section 8.5.
Choose Paid in when you add the payments, as with savings. The future value is then what your starting amount and deposits grow to: $3,000 a year for 5 years at 4% grows to $16,248.97.
Solving for the rate or the time
For a single amount, the rate and the time have closed formulas. If $15,000 grows to $25,000 in 8.5 years, the yearly rate is 6.194%; at 6% a year, it takes 8.77 years. With payments, there is no formula for the rate, so the calculator searches for it: it starts with a wide range of rates, checks which half the answer lies in, and repeats until the values fit to a fraction of a cent. Given the $32,000 loan and its $973.50 payment, it finds 6.00%. In this setup a higher rate always moves the result in the same direction, so only one rate can fit and the answer is never ambiguous.
Compounding and payment frequency
The rate per payment period depends on how often interest compounds and how often you pay. As section 8.4 shows, compounding more than once a year makes the effective annual rate higher than the stated rate: 1.5% a month is 19.56% a year, not 18%. OpenStax Contemporary Mathematics gives the effective annual yield as (1 + r ÷ m)m − 1 for a rate r compounded m times a year. The calculator spreads that effective rate evenly over your payment periods:
| 6% a year, compounded | Monthly rate | Effective annual rate |
|---|---|---|
| Yearly | 0.4868% | 6.000% |
| Quarterly | 0.4975% | 6.136% |
| Monthly | 0.5000% | 6.168% |
| Daily | 0.5012% | 6.183% |
Growing payments
Some payments rise over time, like a pension with yearly increases or a salary-linked contribution. Under Growing payments, enter how much each payment grows over the one before. The calculator values each payment the way section 9.1 values uneven cash flows, discounting each one to today and adding them up, using the closed form of that sum: PV = PMT × (1 − ((1 + g) ÷ (1 + i))n) ÷ (i − g). $20,000 a year for 20 years at 5% is worth $249,244.21 today; if the payments grow 2% a year, the first still $20,000, they are worth $293,308.04.
How to use the present value calculator
- 1Under Solve for, pick the value you want: Present value, Future value, Payment, Rate or Time.
- 2Enter the other values, how often payments are made and interest compounds, whether the payments are Paid out or Paid in, and whether they come at the end or the start of each period. Use 0 as the payment for a single amount.
- 3Read the answer and the schedule by year or by payment. Use Copy result or Copy link to keep it.
For cash flows that change from year to year, use the NPV and IRR calculator. To see savings grow with regular deposits, try the compound interest calculator, and for a full loan with payoff date and total interest, the loan calculator.
Sources
- OpenStax, Principles of Finance (Dahlquist and Knight), 7.3 Methods for solving time value of money problems
- OpenStax, Principles of Finance, 8.2 Annuities (ordinary annuity, annuity due, worked examples)
- OpenStax, Principles of Finance, 8.4 Stated versus effective rates
- OpenStax, Principles of Finance, 8.5 Equal payments with a financial calculator and Excel (loan payment example)
- OpenStax, Principles of Finance, 9.1 Timing of cash flows (present value of uneven cash flows)
- OpenStax, Contemporary Mathematics, 6.4 Compound interest (effective annual yield)
Frequently asked questions
What is present value?
Present value is what a future amount or a series of payments is worth today, at a given interest rate. Money you get later is worth less than the same amount now, because money you have now could earn interest in the meantime. At 5% a year, $50,000 due in 5 years is worth $39,176.31 today.
What is the present value formula?
For a single amount, PV = FV ÷ (1 + i)^n, where i is the interest rate per period and n the number of periods. For equal payments at the end of each period, PV = PMT × (1 − (1 + i)^−n) ÷ i. The calculator adds both when you have a lump sum and payments, and multiplies the payment part by (1 + i) when payments come at the start of each period.
What is the difference between an ordinary annuity and an annuity due?
In an ordinary annuity, each payment comes at the end of the period, as with most loans. In an annuity due, it comes at the start, as with rent or lease payments. Each payment of an annuity due is received one period earlier, so its present value is (1 + i) times higher: $25,000 a year for 5 years at 8% is worth $99,817.75 as an ordinary annuity and $107,803.17 as an annuity due.
How do I find the interest rate or the number of years?
Choose Rate or Time under Solve for, and enter the other values. There is no closed formula for the rate when there are payments, so the calculator finds it numerically: it narrows the range between two rates step by step until the values fit to a fraction of a cent. A higher rate always moves the result in the same direction, so only one rate fits.
Why do compounding and payment frequency both matter?
The rate per payment period depends on both. A 6% rate compounded monthly gives 0.5000% a month; compounded yearly, the same 6% gives 0.4868% a month, because it has to grow to exactly 6% over 12 months. Banks often state a yearly rate with its compounding, so enter both as given.
How is this different from NPV?
Present value here assumes equal or steadily growing payments. Net present value discounts a list of cash flows that can be different every year, including the money you put in at the start. For uneven cash flows, use the NPV and IRR calculator.