Present Value of a Single Sum: Formula and Examples

The present value of a single sum, also called the present value of a single amount or lump sum, is what one future payment is worth today. Calculate it as PV = FV ÷ (1 + i)^n, where FV is the future amount, i is the rate per period, and n is the number of periods.

Discounting reverses compound growth. It finds the starting amount that would grow to the future amount at the stated rate.

For Intermediate Accounting students, the key is the measurement date. A future dollar amount and a current dollar amount are not directly comparable until they are expressed at the same date.

What is the present value of a single sum?

Present value (PV) is the amount at the starting date. Future value (FV) is the amount at the later date. The periodic rate, i, applies to one compounding interval, and n counts those intervals. A discount rate is the rate used to translate the future amount into its current equivalent.

The factor expresses the current equivalent of one future dollar. The California State Board of Equalization explains the same idea under the name present worth of one. This calculation assumes one rate and one future payment. It gives you the math, not the accounting rule that applies to a specific transaction.

What is the difference between present value and future value?

For a positive rate and positive elapsed time, present value is smaller than the corresponding future amount. The values describe the same economic amount at different dates. At a zero rate they are equal. See future value of a single sum for the forward calculation and an annual growth schedule.

Worked example: how much must you set aside today?

Hypothetical example. Cedar Supply needs one payment of $15,000 in four years. Assume that 6% compounded annually is the appropriate rate, with no other payments, fees, or taxes along the way. How much must it set aside today?

Here is the timeline, with the deposit growing 6% a year:

Today: $11,881.40 → End of Year 1: $12,594.28 → End of Year 2: $13,349.94 → End of Year 3: $14,150.94 → End of Year 4: $15,000.00

Present value moves backward along this line, across four annual periods. The difference of about $3,118.60 is the compound interest earned over the four years.

Check the answer by multiplying the unrounded present value by 1.06^4, which is 1.26247696. It returns $15,000. A tiny difference after using the rounded $11,881.40 is normal. This reverse check catches many incorrect factors and misplaced exponents.

How to use a present value factor table

Select the present value of 1 table, then find the 6% column and the four-period row. A five-decimal table gives approximately 0.79209. Multiplying $15,000 by 0.79209 gives $11,881.35, slightly different from the unrounded calculation.

Here is a short present value of 1 table with five-decimal factors:

If a problem supplies a factor, use that factor. Small differences like $11,881.35 versus $11,881.40 come from rounding, not from a mistake.

Do not use a present value annuity factor. An annuity represents repeated equal payments, while Cedar has one payment. Do not divide by the present value factor either: that would move the amount forward. Multiply a future amount by its present value factor, or divide by its corresponding future value factor.

How the rate and waiting time affect present value

Hold the future amount constant. A higher positive rate lowers the amount needed today because the starting funds grow more quickly. A longer wait also lowers present value when the positive rate stays unchanged.

Each row changes one assumption at a time. On homework, use the rate the problem gives you or supports. Do not pick a rate just to reach the answer you want.

For a 6% nominal annual rate compounded semiannually over four years, the matching inputs would be i = 3% and n = 8. Review how to match compounding periods and rates if the quoted annual rate causes confusion.

How do you calculate present value in Excel?

For Cedar Supply, enter =PV(6%,4,0,15000). Excel returns approximately −$11,881.40. The negative sign represents the cash deposit paid out today to obtain a positive future balance. Ignore the minus sign and you have the deposit you need. It is not a loss.

Payment (PMT) is zero because the example has no periodic deposits or withdrawals. Microsoft’s official PV function documentation explains its inputs, consistent period units, and cash-flow signs.

Common present value mistakes

Subtracting simple interest from the future amount. Discounting divides by a compound growth factor. Subtracting FV × rate × years does not undo compound interest.

Ignoring the required date. “Present” means the valuation date selected in the problem. Count only the intervals between that date and the cash flow. If both present and future amounts are given, use the single-sum method for finding an unknown rate or time.

Mismatching the rate and the periods. The rate and n must use the same period. For $15,000 due in four years at 6% compounded semiannually, i = 3% and n = 8 give $11,841.14. Using 6% with 8 periods gives $9,411.19, which is far too low.

Where will you use present value in Intermediate Accounting?

Single-sum present value is more than a homework formula. It shows up when a company signs a long-term note with no stated interest rate.

FASB ASC 835-30 covers this situation. When no reliable price is available for the asset or the note, you find the note’s present value by discounting its future payment at an imputed rate. An imputed rate is a rate you assign because the note does not state a reasonable one. It is generally what the borrower would pay for similar financing elsewhere.

Suppose Cedar Supply buys equipment today by signing a four-year, $15,000 note with no stated interest. No reliable price is available for the equipment or the note, and Cedar could borrow on similar terms at 6%. The present value is the same $11,881.40 from the worked example.

Entry on the purchase date:

The $3,118.60 discount is interest Cedar will recognize over the four years. On the balance sheet, it is shown as a direct deduction from the note’s face amount.

Each year’s interest is 6% of the note’s beginning carrying amount:

Each year’s interest is rounded to the nearest cent before calculating the ending carrying amount.

Entry at the end of Year 1:

The rate is set on the day the note is issued. If market rates change later, Cedar keeps using 6%. Normal supplier payables on customary terms of about a year or less are outside this imputation guidance.

The same discounting step also sits inside bond pricing, where the face amount due at maturity is a single sum.

For more detail, see Deloitte’s roadmap on debt subject to ASC 835-30. To keep building this skill, explore the Intermediate Accounting course.

Key takeaways

• Present value is what one future amount is worth today.
• The formula is PV = FV ÷ (1 + i)^n, or PV = FV × present value factor.
• The rate and n must use the same period. For 6% compounded semiannually over four years, i = 3% and n = 8.
• With a positive rate, a higher rate or a longer wait lowers present value.
• To check your answer, grow it forward: PV × (1 + i)^n should return the future amount.

Back to In this lesson

Three practice questions with answers

Each question is hypothetical and assumes no other payments along the way.

1. Discount one payment

What is the present value of $8,000 due in two years at 5% compounded annually?

2. Use the supplied factor

A $25,000 receipt is due in six periods. At 7% per period, the supplied present value factor is 0.66634. What is its present value?

3. Predict the direction

A fixed payment remains due in four years, but its discount rate rises from 5% to 7%. Does present value rise or fall?

Frequently asked questions

Are discounting and compounding opposites?

Yes, when they use the same rate, periods, and cash-flow assumptions. Compounding carries an amount forward; discounting brings it back.

Why is the present value factor below one?

For a positive rate and at least one period, the compound growth factor exceeds one. Its reciprocal, which is 1 divided by that factor, is therefore below one. At a zero rate the factor is one.

Is present value the same as fair value?

Not automatically. Fair value is defined in FASB ASC 820, and present value is one technique that can estimate it. The two match only if the cash flows and rate reflect market participant assumptions.

What is the difference between the present value of 1 and the present value of a single sum?

The present value of 1 is the factor for one future dollar. The present value of a single sum is that factor multiplied by your actual future amount.

What is the difference between a single sum and an annuity?

A single sum is one payment at one date. An annuity is a series of equal payments made at equal time intervals, so it uses a different factor.

How do I find present value with semiannual compounding?

Divide the annual rate by two and multiply the years by two. For $15,000 due in four years at 6%, use i = 3% and n = 8, which gives $11,841.14.

About the author

Mansour Farhat, CPA, CIA, DBA, is the founder of Farhat Lectures and its YouTube channel. He holds a Doctor of Business Administration from Temple University and a Master of Accountancy from Bloomsburg University. He teaches accounting courses and exam prep for students and for CPA, CMA, and EA candidates. Read his full background.