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Equal Payment Present Value Calculator

Value a level payment stream today.

Result

$7,721.73
$10,000.00

How it is calculated

The tool values an ordinary annuity: equal payments made at the end of each period. The formula is PV = PMT × (1 − (1 + r)−n) ÷ r, where PMT is the payment per period, r is the rate per period as a decimal (5 % = 0.05) and n is the number of periods. The rate and the periods must use the same time unit: a monthly payment needs a monthly rate. If the rate is empty or exactly 0, the tool skips discounting and returns payment × periods. The second result, total paid, is that undiscounted sum. Payment and periods must be above zero. A negative rate is allowed (it makes the present value larger than the total), but a rate of −100 % or below gives no result. Payments at the start of each period (an annuity due) are not covered and would be worth more. The result is in dollars.

Worked example

You will receive 1,000 at the end of each year for 10 years, discounted at 5 % a year. Discount factor: 1.05−10 = 0.613913. Then 1 − 0.613913 = 0.386087, divided by 0.05 gives 7.72173. Present value: 1,000 × 7.72173 = $7,721.73. The payments add up to $10,000.00 in total, so discounting makes the stream worth about 2,278 less in today's money.

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Common mistakes

  • Entering an annual rate with monthly payments. A 5 % annual rate must be turned into a monthly rate (about 0.4 %) when the periods count months, and ten years then means 120 periods. Check: 1,000 a month for 120 months at 0.4 % a month is worth $95,155.97, not $120,000.00.
  • Typing the rate as a decimal. 0.05 means 0.05 %, not 5 %, because the box is already in percent. With 0.05 the ten payments of 1,000 are worth $9,972.55, almost the plain sum.
  • Assuming the first payment is made today. The formula treats every payment as arriving at the end of its period, so payments made at the start of each period are worth more than the result.
  • Confusing present value with the sum of the payments. The second figure is the plain total, and the present value is lower whenever the rate is above zero.
  • Using a loan's interest rate as the discount rate when judging an investment. The discount rate should reflect what you could earn elsewhere, and the result changes a lot with it.

About this calculator

The present value of an ordinary annuity answers a core finance question: what is a stream of equal future payments worth in today’s money, given a discount rate? The formula is PV = PMT × [1 − (1+r)⁻ⁿ] / r, where PMT is the periodic payment, r is the periodic interest (discount) rate, and n is the number of payments — it works because money received later is worth less than money received now, and this formula compresses every future payment’s diminished value into a single lump sum.

This is the exact math behind valuing a loan, a lease, or a bond’s coupon payments, and it’s what lets a lender determine how much principal a borrower can be given today in exchange for a promised stream of equal payments at a set interest rate. Retirement planners use the same formula in reverse to figure out how large a lump sum is needed today to fund a fixed monthly pension-style payout for a given number of years, and it underlies how structured settlements and lottery lump-sum buyouts are priced.

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