To calculate present value with a discount rate, divide the future dollar amount by (1 + r) raised to the power of n, where r is the discount rate per compounding period and n is the number of periods between now and the payment. Written out, the formula is PV = FV / (1 + r)n. The arithmetic is simple; the judgment sits in picking r and matching it to the right time unit.
What Each Variable Stands For
- PV is present value, the number you’re solving for.
- FV is future value, the dollar amount you expect to receive or pay later.
- r is the discount rate per compounding period, written as a decimal (5% becomes 0.05).
- n is the total number of compounding periods between now and the future payment.
The logic behind the formula is that money you have today can be invested, so a dollar arriving later is worth less than a dollar in hand. The division reverses the compounding that could have happened in the meantime.
One thing to watch before you plug numbers in: the rate and the period count have to speak the same language. If your discount rate is annual but the money compounds monthly, divide the rate by 12 and multiply the years by 12. A five-year investment compounding monthly means r = annual rate / 12 and n = 60. Mixing an annual rate with monthly periods produces nonsense, and the formula won’t flag it.
A Worked Example
Say you’re owed $10,000 three years from now and want its present value at a 5% annual discount rate.
- Add 1 to the decimal rate: 1 + 0.05 = 1.05.
- Raise to the power of n: 1.05 × 1.05 × 1.05 = 1.157625.
- Divide the future value by that factor: $10,000 / 1.157625 = $8,638.38.
That $8,638.38 is what the future $10,000 is worth today at a 5% rate. Someone offering you $8,638 right now or $10,000 in three years is offering financially equivalent deals at that rate.
Carry as many decimal places as possible through the intermediate steps. Rounding the growth factor to 1.16 instead of 1.157625 gives $8,620.69, an error of nearly $18 on a $10,000 sum. On six- or seven-figure amounts, early rounding creates real discrepancies. Only round the final answer.
Choosing the Discount Rate
The rate is the most influential input in the whole calculation, and there is no universally correct number. Match it to what you’re valuing.
Risk-Free Benchmarks
When the future payment is essentially guaranteed, such as a U.S. Treasury bond, analysts typically start with Treasury yields. As of early 2026, 3-month Treasury bills yield roughly 3.7% and 10-year Treasury notes yield about 4.2%.1Federal Reserve Bank of St. Louis. Market Yield on U.S. Treasury Securities at 3-Month Constant Maturity2Federal Reserve Bank of St. Louis. Market Yield on U.S. Treasury Securities at 10-Year Constant Maturity Pair the Treasury maturity to your time horizon: a payment six months away lines up with a short-term bill, while a payment 20 years out warrants a longer-term rate.
Risk-Adjusted Rates
Cash flows that might not actually arrive deserve higher rates. A corporate project with uncertain revenues calls for a rate reflecting both the time value of money and the probability the cash never shows up. Businesses often use their weighted average cost of capital, which blends the cost of equity and the after-tax cost of debt in proportion to how the company is financed. For personal investment analysis, adding two to five percentage points above the risk-free rate is a common starting point for moderately risky opportunities.
How Much the Rate Actually Moves the Answer
Small changes in the discount rate produce surprisingly large swings, and the effect grows with time. Using the same $10,000 payment three years out:
- At 3%: $10,000 / 1.092727 = $9,151
- At 5%: $10,000 / 1.157625 = $8,638
- At 7%: $10,000 / 1.225043 = $8,163
A four-percentage-point spread moves the present value by almost $1,000 on a $10,000 payment just three years away. Stretch the horizon and the effect intensifies. A $100,000 lump sum due in 20 years is worth about $45,639 at 4% but only $31,180 at 6%. Same payment, same date, $14,459 gap. Picking the rate carefully matters more than getting the arithmetic perfect.
Doing It in a Spreadsheet
Excel and Google Sheets both have a built-in PV function that handles the compounding automatically. The syntax is the same in both:3Microsoft Support. PV Function4Google Docs Editors Help. PV Function
=PV(rate, nper, pmt, fv, type)
- rate is the discount rate per period (0.05 for 5% annual).
- nper is the total number of compounding periods.
- pmt is the periodic payment. Enter 0 for a single lump sum.
- fv is the future value you’re discounting back.
- type is optional. Use 0 (or leave blank) for end-of-period payments, 1 for beginning.
For the $10,000 example at 5% over three years, enter =PV(0.05, 3, 0, 10000). The result appears as -$8,638.38. The negative sign isn’t an error. Spreadsheets treat present value as a cash outflow, the amount you’d need to invest today to receive $10,000 later. To flip the sign, either enter the future value as negative or wrap the formula: =-PV(0.05, 3, 0, 10000).
When Payments Vary
For a series of unequal cash flows, use NPV instead. In Google Sheets the syntax is =NPV(discount, cashflow1, cashflow2, …), with each argument representing a different period’s payment.5Google Docs Editors Help. NPV Function NPV assumes the first cash flow arrives one period from now. If you have an upfront cost at time zero, subtract it outside the formula: =NPV(rate, future cash flows) – initial cost.6Microsoft Support. NPV Function
Using a Financial Calculator
Dedicated financial calculators like the Texas Instruments BA II Plus use labeled keys for each variable. For a single lump sum:
- Enter the number of periods and press N.
- Enter the annual rate as a whole number (5, not 0.05) and press I/Y.
- Enter the future value and press FV.
- Press 0 then PMT since there are no periodic payments.
- Press CPT then PV.
The result shows as a negative number for the same cash-direction reason spreadsheets do. A display of -8,638.38 means the math worked. Clear the previous entries before starting a new problem (on the BA II Plus, press 2nd CLR TVM). Calculators carry old values in memory, and skipping the clear step silently corrupts the next result.
Present Value of a Stream of Payments
The basic formula covers a single lump sum, but many situations involve recurring payments: annuity income, lease payments, structured settlements, bond coupons. For equal periodic payments, the modified formula is:
PV = PMT × [(1 − (1 + r)−n) / r]
PMT is the payment amount, r is the discount rate per period, and n is the number of payments. The bracketed expression is the annuity factor, and it spares you from discounting each payment separately and adding them up.
If you’ll receive $2,000 a year for 10 years at a 6% discount rate, the annuity factor is (1 − 1.06−10) / 0.06 = (1 − 0.55839) / 0.06 = 7.36009. Multiply by $2,000 and the present value is $14,720.18. In a spreadsheet the same calculation is =PV(0.06, 10, 2000), with fv left at 0.
End of Period or Beginning of Period
The formula above assumes payments arrive at the end of each period (an ordinary annuity), which is how most bonds and settlement payments work. When payments arrive at the beginning (an annuity due, common with lease payments), the present value is slightly higher because each payment sits one period closer to today. Multiply the ordinary annuity result by (1 + r) to convert, or change the type argument in the spreadsheet formula from 0 to 1: =PV(0.06, 10, 2000, 0, 1).
When the IRS Picks the Rate
For some tax filings you don’t get to choose the discount rate. Under Internal Revenue Code Section 7520, the IRS publishes a monthly rate used to value annuities, life estates, and remainder interests for estate, gift, and income tax purposes. The rate equals 120% of the applicable federal midterm rate, rounded to the nearest 0.2%.7Internal Revenue Service. Section 7520 Interest Rates For the first three months of 2026, the Section 7520 rate sits between 4.6% and 4.8%. Using a different rate on these filings will get the return rejected, so this is the one context where the discount rate is not a matter of judgment at all.