Walking through the sample
Load sample on the Dated amounts tab sets up a settlement paid in three parts: $10,000 in one year, $10,000 in three years, and $30,000 in five years. The payer also offers $38,000 today to close the matter. The discount rate is 6% a year.
- The year 1 payment is worth $9,433.96 today. One year of waiting costs about $566.
- The year 3 payment is worth $8,396.19. Same $10,000, two more years of waiting, about $1,000 less.
- The year 5 payment is worth $22,417.75. The largest amount loses the most, $7,582, because it sits furthest out.
Together the $50,000 of payments is worth $40,247.90 today. That beats the $38,000 offer by $2,247.90, so at 6% waiting wins.
Now look at the row of nearby rates. At 7% the payments are worth $38,898.36, still above the offer. At 8% they drop to $37,615.08, below it. The break-even line shows exactly where the answer flips: 7.69%. If you would put the $38,000 somewhere earning more than 7.69% a year, take the cash. If the best place for the money pays less, wait for the payments.
Cash now or more money later?
Most people land on this page with a choice in front of them: a lottery lump sum or yearly installments, a pension buyout or monthly checks, a buyer paying less now or more on terms. Present value turns both sides into today's dollars so you compare like with like.
Take a plain case. You are offered $50,000 now or $65,000 in five years. The break-even rate is 5.39%.
Discount at 4%
$53,425.26
The future $65,000 is worth more than $50,000 today. If your best option for the cash is a savings account paying 4%, wait.
Discount at 7%
$46,344.10
The future $65,000 is now worth less than the $50,000 offer. If you would pay down a 7% loan with the cash, take it.
The payment stream works the same way. The Regular payments sample sets $500 a month for 10 years against a $45,000 lump sum. At 5% compounded monthly the payments are worth $47,140.68, so the monthly checks win by about $2,100. The break-even sits at 6.02%. Switch timing to the start of each period and the value rises to $47,337.09, since every check arrives a month sooner.
The table under the result shows the decay year by year. Year 1 of those payments is worth $5,840.61 today. Year 10 pays the same $6,000 and is worth $3,727.62.
Choosing a discount rate
The rate decides the answer more than any other input, and no single correct rate exists. Use the return on the best thing you would realistically do with the money instead. Some starting points:
- Savings or Treasury yield
- For guaranteed payments, such as a court-ordered settlement or a pension from a solid plan, the rate on a high-yield savings account or a Treasury bond of similar length fits.
- Interest rate on your debt
- If the cash would go toward a credit card, car loan, or mortgage, use that loan's rate. Paying off 7% debt is a guaranteed 7% return.
- Expected investment return
- If you would invest the lump sum in stocks, people often use 6% to 8%. Remember the stock return is not guaranteed while the payments might be, so this rate tilts the decision toward taking cash.
- Payer risk added on top
- A promise from a small private buyer or a struggling company deserves a higher rate than a promise from a government. Add a few points for each payment you are less sure will arrive.
Run two or three rates and read the nearby-rates row. When the decision holds across all of them, you have a clear answer. When it flips inside your plausible range, the choice is close and other factors, like taxes or your need for cash today, should settle it.
The present value formula
Each amount is divided by the growth it would have earned between today and its payment date:
single amount: PV = FV / (1 + r/n)^(n × t)continuous: PV = FV × e^(-r × t)level payments: PV = PMT × (1 - (1 + i)^(-N)) / i
start-of-period: multiply the level-payment result by (1 + i)r is the yearly rate as a decimal, n is compounding periods per year, and t is years until payment. For level payments, i is the rate per payment period and N is the number of payments. The calculator does not use the shortcut formula. It discounts every payment on its own date and adds them up, which gives the same total and also handles a monthly payment with quarterly compounding without a conversion step.
The Factor column is the 1 / (1 + r/n)^(n × t) part. Multiply any amount by its factor and you get its present value. On the Regular payments tab the column shows the average factor across the payments in each year.
Discount factors at a glance
| Rate | 1 year | 5 years | 10 years | 20 years | 30 years |
|---|---|---|---|---|---|
| 3% | 0.9709 | 0.8626 | 0.7441 | 0.5537 | 0.4120 |
| 5% | 0.9524 | 0.7835 | 0.6139 | 0.3769 | 0.2314 |
| 8% | 0.9259 | 0.6806 | 0.4632 | 0.2145 | 0.0994 |
| 10% | 0.9091 | 0.6209 | 0.3855 | 0.1486 | 0.0573 |
Read across a row and the long end stands out. $100,000 due in 30 years is worth $41,198.68 at 3% but only $13,136.71 at 7%. For far-off money, four points of rate cut the answer to a third. Compounding frequency matters far less: $10,000 due in 10 years at 6% is worth $5,583.95 with yearly compounding and $5,496.33 with monthly, an $88 gap.
What the number leaves out
- One flat rate for the whole term. Real rates move. A 20-year comparison made at today's rate is a reasonable estimate, not a forecast.
- Taxes. A lump sum often lands in one tax year at a higher bracket, while installments spread the income out. Two options with equal present value before tax can differ by thousands after it. Check with a tax advisor for large amounts.
- Inflation is folded into the rate. Enter amounts in the dollars you will receive and use a normal rate. If you want everything in today's buying power, subtract expected inflation from the rate, or check the drop with the inflation calculator.
- Payments that might not arrive. The math assumes every payment shows up. Raise the rate for shaky payers rather than trusting the face value.
- Mixed signs have more than one break-even. With costs and income mixed together, the break-even search reports one rate where the totals match, and a second one sometimes exists. For full project analysis with an investment up front, an IRR tool reads better.
- Size limits. The Dated amounts list holds 60 rows and dates up to 200 years out. The Regular payments tab runs up to 100 years.