Present Value Calculator
Present Value of Future Money
- Total Interest
- $441.61
Present Value of Periodical Deposits
- FV (Future Value)
- $1,318.08
- Total Principal
- $1,000.00
- Total Interest
- $318.08
Schedule
| Period | Deposits | Interest | End balance |
|---|---|---|---|
| 1 | $100.00 | $0.00 | $100.00 |
| 2 | $200.00 | $6.00 | $206.00 |
| 3 | $300.00 | $12.36 | $318.36 |
| 4 | $400.00 | $19.10 | $437.46 |
| 5 | $500.00 | $26.25 | $563.71 |
| 6 | $600.00 | $33.82 | $697.53 |
| 7 | $700.00 | $41.85 | $839.38 |
| 8 | $800.00 | $50.36 | $989.75 |
| 9 | $900.00 | $59.38 | $1,149.13 |
| 10 | $1,000.00 | $68.95 | $1,318.08 |
This present value calculator discounts a future amount, or a series of equal periodic deposits, back to what it is worth today at the interest rate you choose.
Present Value
Present value is today's worth of money you will receive later. It runs compounding in reverse: instead of growing a sum forward, you discount a future amount back by the rate you could earn in the meantime. At 6% a year, $1,000 due in ten years is worth $558.39 today, because $558.39 invested now at 6% would grow to $1,000 by then.
PV = FV ÷ (1 + i)ᴺ
- PV
- present value
- FV
- amount received in the future
- i
- discount rate per period, as a decimal
- N
- number of periods
For N equal payments of PMT at the end of each period, PV = PMT × [1 − (1 + i)⁻ᴺ] ÷ i. Multiply by (1 + i) when payments come at the start of each period.
Net Present Value
Net present value (NPV) extends the idea to a whole project. You discount every expected cash flow, positive or negative, to today and add them up, counting the up-front cost as a negative amount at time zero. A positive NPV means the project returns more than the discount rate after paying back its cost; a negative NPV means you would do better investing at that rate instead.
Suppose a machine costs $2,000 and saves $600 a year for four years. At an 8% discount rate the savings are worth $600 × (1 − 1.08⁻⁴) ÷ 0.08 ≈ $1,987.27 today, so NPV ≈ −$12.73 and the purchase falls just short. At 7% the same savings are worth about $2,032.27 and NPV turns positive. The rate at which NPV is exactly zero is the internal rate of return.
Businesses use NPV to rank projects and decide which ones to fund, typically discounting at their cost of capital. Individuals use the same logic, often informally, when they weigh a lump-sum pension buyout against monthly payments or compare a lottery's cash option with its annuity.
The Time Value of Money
Money available now can be invested, spent or saved against emergencies, so people demand something extra to wait for it. That extra is interest, and it is why a future sum must be discounted before it can be compared with money in hand. The higher the rate and the longer the wait, the less a future amount is worth today: $1,000 in ten years is worth $744.09 at 3% but only $385.54 at 10%.
| Today's value of $1,000 due in | 3% rate | 6% rate | 10% rate |
|---|---|---|---|
| 5 years | $862.61 | $747.26 | $620.92 |
| 10 years | $744.09 | $558.39 | $385.54 |
| 20 years | $553.68 | $311.80 | $148.64 |
| 30 years | $411.99 | $174.11 | $57.31 |
Frequently asked questions
How do you calculate present value?
Divide the future amount by (1 + rate) raised to the number of periods. $1,000 in 10 years at 6% is $1,000 ÷ 1.06^10 = $558.39.
What discount rate should I use?
Use the return you could reasonably earn elsewhere at similar risk: a savings or Treasury rate for safe cash flows, a higher rate for uncertain ones.
What is the present value of $100 a year for 10 years at 6%?
$736.01 if paid at the end of each year, or $780.17 if paid at the start of each year.
What is the difference between present value and NPV?
Present value discounts future cash inflows. NPV subtracts the up-front cost as well, so it tells you whether an investment beats the discount rate.
What is the formula for the present value of an annuity?
For equal payments at the end of each period, PV = PMT × [1 − (1 + i)^−N] ÷ i. For payments at the start of each period, multiply that result by (1 + i). $100 a year for 10 years at 6% has a present value of $736.01, or $780.17 if each payment comes at the start of the year.
What is a present value factor?
It is the present value of $1 received in the future: 1 ÷ (1 + i)^N. At 6% for 10 years the factor is about 0.5584, so any amount due in 10 years is worth 55.84% of its face value today. Multiply a future amount by the factor to discount it.
How do I calculate present value in Excel?
Use =PV(rate, nper, pmt, [fv], [type]), with the rate per period and type 1 for payments at the start of each period. =PV(6%, 10, 0, -1000) returns $558.39, and =PV(6%, 10, -100) returns $736.01. Excel shows the result with the opposite sign of the cash flows you enter, so enter payments as negative numbers to get a positive present value.
Results are estimates for educational purposes and are not financial, tax or legal advice. Confirm figures with a qualified professional or your lender.
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