Present Value Calculator
Calculate the present value of a future sum or annuity. PV = FV / (1+r)^n for a lump sum. PV = PMT × [1 − (1+r)^(−n)] / r for an annuity. Shows time value of money.
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How It Works
Enter future value (FV), annual discount rate (r), and time periods (n). PV = FV / (1+r)^n. Example: $10,000 promised in 8 years at 5% discount rate: PV = 10000 / (1.05)^8 = $6,768. This is the maximum you should pay today for the right to receive $10,000 in 8 years.
PV = FV / (1+r)^n | discount factor = 1/(1+r)^n$10,000 in 8yr at 5%: PV = 10000/1.4775 = $6,768Enter periodic payment (PMT), rate per period, and number of periods. PV = PMT × [1 − (1+r)^(−n)] / r. Example: $1,000/year for 10 years at 6%: PV = 1000 × [1 − 1.06^(−10)] / 0.06 = $7,360. This is the lump sum equivalent of that income stream.
PV annuity = PMT × [1−(1+r)^(−n)] / r$1,000/yr for 10yr at 6%: PV = $7,360Higher discount rate → lower PV. Longer time → lower PV. A $100,000 payment in 20 years: at 3% discount → PV=$55,368, at 6% → PV=$31,180, at 10% → PV=$14,864. The calculator lets you adjust both variables to see how sensitive the PV is — useful for uncertain future cash flows.
Higher r or longer n → dramatically lower PV$100k in 20yr: 3%=$55k, 6%=$31k, 10%=$15kA bond with $1,000 face value, 5% annual coupon, 10-year maturity: PV = PV of coupons (annuity: $50/yr for 10yr) + PV of face value ($1,000 in 10yr). At 5% market rate: bond price = $1,000. At 7% market rate: bond price drops to $859. Enter each component separately to price any bond.
Bond price = PV(coupons) + PV(face value)5% coupon, 10yr, 7% market rate: price=$859Enter annual net rental income as the annuity payment, required return rate, and holding period. The PV is the property's investment value. If market price exceeds PV at your required return, the property is overpriced for your goals. At 8% required return, $20,000/yr for 20 years: PV = $196,363.
Property value = PV of net rental income stream$20k/yr rent, 8% required return, 20yr: PV=$196,363Quick Reference
Verify these in the calculator above.
Lump sum
$10,000 in 8yr at 5%
PV = $6,768
Annuity
$1,000/yr for 10yr at 6%
PV = $7,360
Long term
$100k in 20yr at 6%
PV = $31,180
High rate
$100k in 20yr at 10%
PV = $14,864
Bond
Bond: 5% coupon, 10yr, 7% market
Price = $859
Real estate
$20k/yr rent, 8%, 20yr
Property value $196k
Rate effect
Double the discount rate
PV roughly halves
Time effect
Same PV at double time
Much lower FV needed
Tips & Shortcuts
Use the same time units for rate and periods — if the rate is monthly, periods must be months. A 6% annual rate used monthly = 0.5% per month.
For comparing cash flows at different times, always convert to PV — this is the only valid way to compare money at different points in time.
The discount rate represents the opportunity cost. If you can earn 7% elsewhere at similar risk, use 7% as your discount rate.
PV decreases exponentially with time and rate — a slight increase in either has a large effect on PV of distant cash flows.
For annuities starting next period (ordinary annuity, e.g. loan payments), use the standard formula. For annuities starting immediately (annuity due), multiply by (1+r).
Common Mistakes
Using annual rate for monthly periods without adjusting
If cash flows are monthly, the rate must be monthly. Monthly rate = annual rate / 12. Using 6% annual for monthly periods (should be 0.5%/month) dramatically overstates the discount and understates PV.
Confusing PV with NPV
PV discounts future cash flows. NPV = PV of future cash flows − initial investment. PV > 0 for any positive future cash flow. NPV > 0 means the investment creates value.
Using nominal rate when cash flows are inflation-adjusted
If future cash flows are already expressed in real (today's) dollars, use the real rate (nominal − inflation). If in nominal dollars, use the nominal rate.
Forgetting that higher discount rates favor receiving money sooner
At 10%, $1,000 received today is worth exactly $1,000. In 5 years it is worth only $621 today. High discount rates make near-term cash flows much more valuable than distant ones.
Not matching periods to cash flow frequency
For monthly annuity payments, use monthly rate and total months. Annual rate/12 = monthly rate, annual periods × 12 = monthly periods. Mixing yearly rate with monthly periods is a common error.
Frequently Asked Questions
Present value (PV) is the current worth of a future sum of money, discounted at a given rate. $1,000 received in 5 years is worth less than $1,000 today because money today can be invested to grow. At 5% discount rate, $1,000 in 5 years: PV = 1000 / (1.05)^5 = $783.53 today.
PV (Present Value) discounts a single future value or stream of equal payments. NPV (Net Present Value) discounts a series of unequal cash flows and subtracts the initial investment. NPV is the key capital budgeting tool; PV is used for valuing bonds, annuities, and simple future payments.
The discount rate reflects the opportunity cost of money — what you could earn elsewhere (time value of money) plus risk. For risk-free investments (Treasury bonds), use the risk-free rate (~4-5%). For business projects, use the company's cost of capital (WACC, typically 8-12%). Higher risk → higher discount rate → lower PV.
A bond's price = PV of all future coupon payments (annuity) + PV of face value (lump sum). If interest rates rise after issuance, the discount rate increases and bond PV falls — this is why bond prices move inversely to interest rates.
PV annuity = PMT × [1 − (1+r)^(−n)] / r. Example: $500/month for 10 years at 6% annual (0.5% monthly): PV = 500 × [1 − (1.005)^(−120)] / 0.005 = $45,036. This is the lump sum that would fund those payments.
PV calculates what a rental property is worth based on future rental income. Annual rent of $24,000 for 20 years, discounted at 8%: PV = $235,452. If a property generates $24,000/yr in rent and you need an 8% return, you should pay no more than $235,452.
Inflation acts like a discount rate, eroding future purchasing power. At 3% inflation, $1,000 in 10 years is worth $744 in today's dollars. For inflation-adjusted PV, use the real interest rate (nominal rate − inflation) as the discount rate.
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