How this calculator works
- Step 1Cash at the ending date₹1,00,000.00A separate lump sum, not a regular payment.
- Step 2Discount each period8%Across 10 annual periods in the default plan.
- Step 3Equivalent today₹46,319.35The amount that would compound to that receipt under this assumption.
Present value puts cash arriving on different dates onto one time basis: today. Each future receipt is divided by its compound-growth factor. A larger positive discount rate gives a smaller equivalent today because each rupee is assumed to grow faster.
The rate is an assumption you supply. This tool does not decide the right discount rate for a risky asset, estimate a market price or assess whether someone will actually pay you.
Worked example: one final receipt
- Number of periods
N = years × payments per year- Single receipt
PV = final receipt ÷ (1 + i)^N- End-of-period receipts
PVpayments = payment × [1 − (1 + i)^(−N)] ÷ i
- irate per payment period 8%
- Nnumber of payment periods 10
- Final receipt at the ending date₹1,00,000.00
- Annual discount rate8%
- Duration in years10
- Separate regular receipts₹0.00
- Final receipt discounted to today₹46,319.35
- Regular receipts discounted to today₹0.00
- Total present equivalent₹46,319.35
The two components add together. If your final payment already includes the regular receipt due that day, separate them before entering amounts. Otherwise, that receipt would be counted twice.
The payment timeline shows both rows at the ending date when a final lump sum and an end-of-period receipt coincide. They are separate cash amounts, not an extra payment introduced by the calculator.
Equal receipts: start or end matters
- End of each year₹99,817.75The first receipt arrives after one full year.
- Start of each year₹1,07,803.17The first receipt arrives today; each payment is discounted for one fewer year.
These examples use equal annual receipts and no final lump sum. An ordinary annuity means equal end-of-period payments. An annuity due means equal start-of-period payments. Start timing multiplies the payment component by one plus the periodic rate.
The separate final receipt always stays at the ending date. Changing regular-payment timing does not move that final receipt or change the number of receipts.
Match the rate to the payment period
Nominal rates divide by frequency; effective annual rates preserve the entered full-year change.
For nominal annual rate r and f payments per year, the periodic rate is r divided by f. For an effective annual rate, it is the f-th root of one plus r, minus one. The tool shows both the periodic and effective annual rates.
Payments and compounding have the same frequency here. Annual, half-yearly, quarterly and monthly are available. When switching frequency, check the payment amount too: keeping the same amount creates a different annual cash total.
Zero and negative discount rates
- Zero discount rate₹1,00,000.00No discounting: the present equivalent equals the cash total.
- Negative discount rate₹2,86,797.20The present equivalent exceeds the final receipt under steady shrinkage.
At zero rate, the payment component is simply payment times payment count; there is no division by zero. A negative rate reverses the usual discount relationship. This mathematical case is allowed, but it does not simulate fluctuating returns.
Read the result without over-interpreting it
A discount-rate equivalent is not automatically an inflation-adjusted purchasing-power figure.
The headline and all timeline equivalents refer to today. The undiscounted cash total just adds receipts without considering dates. Their difference describes the effect of your chosen rate; it is not a fee, tax bill or realised loss.
The model assumes unchanged rates and equal payments over whole years. It excludes tax, charges, inflation adjustments, missed receipts and default risk. For irregular dated cash flows or mixed inflows and outflows, use a model designed for those questions.
Related time-value tools
Present value runs time backwards. Growing money forwards, or solving for other unknowns, has its own tool.
To grow a sum and deposits to a future date, use the future value calculator. The annuity calculator gives both values for equal payments, and the financial calculator solves for the payment, rate or term too.
To see what a future price means in today’s money, try the inflation calculator.
Common mistakes
Mistake: Enter the same final payment as both a regular and separate final receipt.
Instead: Split amounts so each rupee appears once.
Mistake: Use a yearly payment amount with monthly frequency.
Instead: Enter the amount received each selected period.
Mistake: Assume start timing moves every receipt, including the final lump sum.
Instead: Check the timeline: only regular receipts move earlier.
Mistake: Read the result as an investment recommendation.
Instead: Check the rate assumption, risk and exclusions separately.
Sources and independent checks
Each receipt can be discounted separately, then added to check the closed-form answer.
The equations follow OpenStax’s compound-value and annuity treatment. Tests compare closed forms with separate discounted sums, verify start/end dates and reconstruct single-sum round trips. CSV uses the same unrounded rows shown in the table. Sources and review details follow.
Read how we test our calculators, or browse more money calculators.