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Tool 9

Investment calculators · Matched periodic assumptions

Present Value Calculator

Created by Arunangshu DasReviewed

Value a future lump sum and equal cash receipts at an explicit rate per period. See discounted components, cash timing and the valuation adjustment.

An equal-period valuation scenario before fees, taxes and inflation. No forecast or personalized financial advice.

Preparing calculator…

Terminal cash, receipt, rate per period and complete period count

Match all three period units

Monthly rate → monthly receipt → count months. No annual-rate conversion or calendar unit is inferred.

Formatting only; no currency conversion or tax rules.

Separate lump sum received at period N; do not include the receipts again. Nonnegative, at most 10^15; explicit zero is allowed.

Equal nonnegative receipt each period, at most 10^15. Enter 0 for a lump sum; blank is not zero.

Effective interest rate used for discounting, greater than −100% through 1000%. Not actuarial discount d or an annual quote unless the period is one year. Use an ordinary minus sign for negative rates.

Whole count 0–36500. For 18 months with monthly rate and payments, enter 18. No fractional periods, dates or leap-day counting.

Both timings include exactly N receipts when N is positive and the receipt is nonzero. Zero periods includes none.

Present value

Enter all four numeric assumptions or load the verified 18-period example.

80 significant decimal digits internally; half-even currency display at 2 places. Tiny nonzero amounts are marked. Inputs stay in browser memory. No per-period cent rounding, mixed inflows/outflows, varying rates or savings-target funding solve.

Value receipts with matching period units

For a monthly rate, enter a monthly receipt and count months. Eighteen monthly periods means 18, not 1.5. No annual-rate conversion is inferred.

Read the complete present value guide

Formula and methodology

q = 1 + R/100; v = 1/q; PV = Fv^N + CΣ(v^k)
End receipts: k=1…N. Beginning receipts: k=0…N−1.
At zero rate: PV=F+CN. At zero periods: PV=F, no recurring receipt.

Set q=1+R/100 and v=1/q. Terminal present value is Fv^N. End-period receipts have present value C×sum(v^k,k=1…N); beginning receipts use k=0…N−1. Add those discounted components to obtain PV. Undiscounted cash is F+CN, and the valuation adjustment is that cash total minus PV. At zero rate PV=F+CN. At zero periods PV=F with no recurring receipt under either timing.

Verified worked examples

Receive a separate 1,000 terminal amount plus 100 at each month-end for 18 months, discounted at 1% per month. Terminal PV is 836.0173141911 and receipt PV is 1,639.8268580892. Combined PV is 2,475.8441722803 (2,475.84 displayed); undiscounted cash is 2,800 and valuation adjustment is 324.1558277197 (324.16 displayed). Moving the same 18 receipts to period starts gives PV 2,492.2424408612 (2,492.24 displayed). A separate exact check: 121 in two periods at 10% per period has PV 100.

Inputs and interpretation

Choose a display market, enter the separate terminal amount and recurring receipt (explicit 0 if absent), rate per period and complete period count. Select beginning or end timing. Inspect the receipt timeline and component values. This values future receipts; it does not solve the initial savings needed to fund a target while contributing deposits. Clear values removes the in-memory scenario.

Assumptions and limitations

The discounting rate, cash receipt and count refer to the same equal period. A monthly rate needs monthly receipts and a count of months. The supplied rate is constant and the receipts are level. No automatic annual conversion, calendar dates, leap-year accrual, day-count adjustment or per-period cent rounding applies. Currency selection changes display only.

Supported domain and common mistakes

F and C range from 0 through 10^15. Rate is greater than −100% and at most 1000% per period. N is a whole count 0–36500. Enter ungrouped decimal points with at most 12 fractional places and 48 characters. PV above 10^30 is rejected without clipping. No fractional periods, changing rates, irregular or mixed-sign flows, perpetuities, taxes, fees, inflation or FX are modeled.

Do not count a terminal amount that already includes the receipts as a separate additional cash flow. Do not enter an annual effective yield as a monthly rate, treat periods as years automatically, or substitute actuarial discount d for effective interest i. A negative rate may give PV above future cash; the negative valuation adjustment is not investment profit. Excel uses opposing cash-flow signs.

Frequently asked questions

Can I value just a lump sum or just regular receipts?
Yes. Enter an explicit 0 receipt to value only the terminal amount, or 0 terminal amount to value only equal receipts. Blank values are not silently treated as zero. Both amounts may be positive when they represent separate cash flows.
Which discounting rate should I enter?
Enter the effective interest rate for exactly one payment period, expressed as a percentage. A monthly receipt needs a monthly rate and count of months. This tool does not select a rate, convert annual quotes or accept actuarial discount d as an equivalent input.
Does beginning timing add another receipt?
No. For N positive periods and a nonzero receipt, both timings include N receipts. Beginning uses indices 0 through N−1 and end uses 1 through N. At zero periods there are no recurring receipts, even beginning timing.
Can present value exceed the undiscounted cash total?
Yes, at a negative discounting rate greater than −100%. The valuation adjustment then becomes negative. At zero rate PV equals undiscounted cash. A negative adjustment is not earned interest or realized profit.
How do I compare this result with Excel PV?
For positive amounts F and C here, compare PV(R/100,N,-C,-F,type), with type 0 for end or 1 for beginning. Excel uses opposing signs for the present amount and future cash. Match periods and assumptions; full spreadsheet compatibility is not guaranteed.
Is this the amount I must save now to reach a target?
For a lump sum alone it is a mathematical discounted equivalent. Adding periodic receipts values additional cash flows; it does not subtract future savings deposits to solve a funding target. Do not use this combined receipt valuation as a savings-plan solver.
Does changing the display currency convert my cash flows?
No. USD, GBP, CAD, AUD and INR change formatting only. Enter all amounts in one currency before calculating. No live exchange rates, market-specific tax calculation or country-specific product rules are applied.

Sources and educational scope

Educational financial arithmetic only, not personalized investment advice, a product quote, an offer valuation or a forecast. Rate selection, credit risk, taxes, fees, inflation and actual agreement terms can materially change a decision. No guaranteed return or independent expert financial review is claimed.

Reviewed . AI-assisted content under operator editorial responsibility; no independent expert financial review is claimed.

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