What Is the Time Value of Money?
The time value of money (TVM) is the idea that a dollar today is worth more than a dollar in the future, because today's dollar can earn interest in the meantime. It's the basis of saving, lending and investing: it tells you what a future amount is worth today, and what today's money can become.
The four values
- Present value: what money is worth today.
- Future value: what it grows to later.
- Interest rate: how fast it grows each year.
- Years: how long it grows.
If you know three of them and how often interest compounds, you can find the fourth. Each tab of the calculator solves for one.
Which calculator should I use?
- This calculator: for one lump sum, with no payments along the way.
- Compound Interest calculator: when you also make regular deposits or withdrawals.
- Annuity Present Value and Annuity Future Value calculators: for a series of equal payments.
- Uneven Cash Flow calculator: for a series of amounts that change each year.
- Investment Growth calculator: to compare one amount at two different rates.
- Rule of 72 calculator: for a quick estimate of how long money takes to double.
How to Calculate the Time Value of Money
All four tabs use one formula, rearranged for the missing value:
- FV: the future value.
- PV: the present value.
- r: the yearly interest rate, as a decimal.
- n: how many times a year interest compounds.
- t: the number of years.
Examples
With yearly compounding (n = 1):
- Present value: $15,000 in 3.5 years at 5.25% is worth $15,000 ÷ 1.05253.5 = $12,540.47 today.
- Future value: $15,000 today at 5.25% for 3.5 years grows to $15,000 × 1.05253.5 = $17,941.91.
- Interest rate: growing $15,000 into $20,000 in 6.5 years takes ($20,000 ÷ $15,000)1 ÷ 6.5 − 1 = 4.53% a year.
- Years: growing $10,000 into $15,000 at 5.25% takes ln($15,000 ÷ $10,000) ÷ ln(1.0525) = 7.92 years, about 7 years, 11 months.
How compounding changes the result
Interest added more often earns interest sooner. The $15,000 above grows to $17,941.91 with yearly compounding, $18,018.51 with monthly compounding and $18,025.49 with daily compounding.
How to Use the Time Value of Money Calculator
"I need $15,000 in 3.5 years, and I can earn 5.25% a year. How much should I set aside today?" This calculator answers that on the Present Value tab.
Let's enter the numbers for this example in each box. They are already filled in when the calculator opens, so you can follow along and then change any box to match your own numbers.
Present Value tab
- Years: Enter 3.5, which is how long until you need the money. It must be greater than 0, up to 1,000.
- Yearly Interest Rate: Enter 5.25, which is the yearly rate in percent. It must be from 0 to 99.99.
- Compounding: Choose Yearly, which is how often interest is added. You can also choose Semi-Annually, Quarterly, Monthly or Daily.
- Future Value: Enter 15,000, which is the amount you want to end with. It must be greater than 0.
The other tabs
- Future Value tab: Enter 3.5 years, a 5.25% rate, Yearly compounding, and 15,000 as the Present Value, which is the money you start with.
- Interest Rate tab: Enter 6.5 years, a Future Value of 20,000, a Present Value of 15,000, and Yearly compounding. If the Future Value is lower, the rate comes out negative.
- Years tab: Enter a 5.25% rate, Yearly compounding, a Present Value of 10,000 and a Future Value of 15,000. The rate must be above 0, and the Future Value must be more than the Present Value.
Calculate and Reset
Click Calculate to see your results. If a box has a problem, such as 0 years, a message pops up under that box instead. With the default numbers on the first tab you get:
- Your Results: a short summary in words: the answer ($12,540.47) and how much of the future value comes from interest.
- Headline: the value the tab solves for.
- Present Value, Future Value, Interest Earned and Effective Annual Rate: $12,540.47, $15,000.00, $2,459.53 and 5.25%. The effective rate includes compounding.
- Growth chart: the present value with interest building on top, up to the future value.
- At each compounding: the tab's answer at each compounding frequency, with yours highlighted. On the Future Value tab, a link opens the Compound Interest calculator, or Compound Daily Interest for daily compounding, with your numbers filled in.
- Yearly Schedule: each year's interest and value. Download Excel saves it with the formulas, so you can change a number and see the schedule update.
- Share Results: a link that opens this calculator on this tab with your numbers filled in. Copy it, or share it on Facebook or X.
Amounts of $1 million or more are shortened, for example $1.25M. Click Reset to put the boxes on the current tab back to their defaults and show the default results again.