Future Value of Money in 9 Minutes
Future value tells you what an amount of money today will grow to after earning interest for a number of years. It is the starting point for the whole time value of money topic, and once you get it, present value is just the same formula run backwards.
Future value explained simply
Future value is what money today grows to after earning compound interest: FV = PV × (1 + r)ⁿ. In the example, $1,000 at 5% for 3 years grows to about $1,157.63.
What this future value lesson covers
- What future value means and why money grows over time
- The future value formula for a single lump sum
- How to calculate FV by hand or on a calculator
- How future value links to present value and NPV
Future value formula, explained
- FV
- future value
- PV
- present value, the amount you have today
- r
- interest rate per period
- n
- number of periods
How to calculate future value step by step (worked example)
You deposit $1,000 today at 5% interest a year. How much will you have in 3 years?
- Write down the inputs: PV = $1,000, r = 5% = 0.05, n = 3.
- Find the growth factor: (1.05)³ = 1.157625.
- Multiply: FV = $1,000 × 1.157625 = $1,157.63 (rounded to the cent).
Answer: About $1,157.63 after 3 years.
Simple interest vs compound interest
| Simple interest | Compound interest | |
|---|---|---|
| Interest is earned on | The original amount only | The original amount plus past interest |
| Formula | FV = PV × (1 + r × n) | FV = PV × (1 + r)ⁿ |
| $1,000 at 5% for 3 years | $1,150.00 | $1,157.63 |
| Used for | Some short-term loans | Savings, investments and most of finance |
Harder future value questions
How long does it take money to double at 5%?
About 14.2 years exactly (ln 2 ÷ ln 1.05). The rule of 72 gives a quick estimate: 72 ÷ 5 = 14.4 years.
What is the same $1,000 worth after 10 years at 5%?
$1,000 × 1.05¹⁰ ≈ $1,628.89. Compounding speeds up over time: the last 7 years add far more than the first 3.
Common future value questions
What is the formula for future value?
For a single amount, FV = PV × (1 + r)ⁿ. PV is what you have today, r is the interest rate per period, and n is the number of periods. The (1 + r)ⁿ part is the growth factor that shows how much each dollar grows.
How do you calculate future value step by step?
Turn the rate into a decimal, add 1, raise it to the power of the number of periods, then multiply by the amount you start with. For $1,000 at 5% for 3 years, that is $1,000 × 1.05³ ≈ $1,157.63.
What is the difference between future value and present value?
Future value moves money forward in time by adding interest. Present value moves money back in time by removing interest, which is called discounting. They use the same formula rearranged: PV = FV ÷ (1 + r)ⁿ.
Does future value use simple or compound interest?
The standard future value formula uses compound interest, so you earn interest on past interest. With simple interest the formula is FV = PV × (1 + r × n) instead, which gives a smaller answer over several years.