Mathwords logoReference LibraryMathwords

Future Value

Future value is the amount of money an investment or deposit will grow to over a period of time, based on a specific interest rate. It tells you what your money today will be worth at some point in the future.

Future value (FV) represents the projected worth of a present sum of money after it has earned interest over a given number of compounding periods. When interest compounds, each period's earnings are added to the principal, so subsequent interest is calculated on a larger balance. Future value is a foundational concept in the time value of money, which holds that a dollar today is worth more than a dollar in the future because of its earning potential.

Key Formula

FV=PV×(1+rn)n⋅tFV = PV \times \left(1 + \frac{r}{n}\right)^{n \cdot t}
Where:
  • FVFV = the future value of the investment
  • PVPV = the present value (initial amount invested or deposited)
  • rr = the annual interest rate (as a decimal)
  • nn = the number of times interest compounds per year
  • tt = the number of years

Worked Example

Problem: You deposit $2,000 in a savings account that earns 6% annual interest, compounded quarterly. What will the account be worth after 5 years?
Identify the values: Write down the known quantities from the problem.
PV=2000,r=0.06,n=4,t=5PV = 2000, \quad r = 0.06, \quad n = 4, \quad t = 5
Substitute into the formula: Plug the values into the future value formula.
FV=2000×(1+0.064)4⋅5FV = 2000 \times \left(1 + \frac{0.06}{4}\right)^{4 \cdot 5}
Simplify inside the parentheses: Divide the annual rate by the number of compounding periods and add 1.
FV=2000×(1.015)20FV = 2000 \times (1.015)^{20}
Evaluate the exponent: Raise 1.015 to the 20th power using a calculator.
(1.015)20≈1.34686(1.015)^{20} \approx 1.34686
Multiply to find FV: Multiply the present value by the growth factor.
FV=2000×1.34686≈2693.71FV = 2000 \times 1.34686 \approx 2693.71
Answer: After 5 years, the account will be worth approximately $2,693.71.

Visualization

Why It Matters

Future value is essential for financial planning. Whether you're comparing savings accounts, evaluating an investment, or estimating how much a college fund will grow, calculating FV helps you make informed decisions about your money. Banks, investors, and retirement planners all rely on this concept to project growth over time.

Common Mistakes

Mistake: Using the interest rate as a percentage instead of a decimal
Correction: Always convert the percentage to a decimal before substituting. For example, 6% should be entered as 0.06, not 6.
Mistake: Ignoring the compounding frequency
Correction: If interest compounds quarterly, you must divide the rate by 4 and multiply the exponent by 4. Using the annual rate and number of years alone gives an incorrect result unless interest compounds once per year.

Related Terms