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Future Value Calculator

Future value measures what a current investment or series of payments will be worth at a specified point in the future, given a rate of return. The lump sum formula is FV = PV x (1 + r)^n, and the annuity formula is FV = PMT x [((1 + r)^n - 1) / r]. A $10,000 lump sum invested at 7% annually for 20 years grows to an estimated $38,697. Select either a lump sum or annuity calculation, enter your values, and see the estimated future value, total contributions, and interest earned.

Quick Answer

A $10,000 lump sum invested at 7% annually for 20 years has an estimated future value of approximately $38,697, with approximately $28,697 in estimated interest earned.

Common Examples

Input Result
$10,000 lump sum at 7% for 20 years Estimated future value: approximately $38,697
$5,000 lump sum at 5% for 10 years Estimated future value: approximately $8,144
$50,000 lump sum at 8% for 30 years Estimated future value: approximately $503,133
$5,000/year annuity at 7% for 20 years Estimated future value: approximately $204,977
$10,000/year annuity at 6% for 30 years Estimated future value: approximately $790,582

How It Works

This calculator uses the time value of money principle: money today is worth more than the same amount in the future because it can earn a return over time.

Lump Sum Future Value:

FV = PV x (1 + r)^n

Where:

  • FV = estimated future value
  • PV = present value (initial investment)
  • r = annual interest rate (as a decimal)
  • n = number of years

This answers the question: “If I invest PV today at rate r, how much will it be worth in n years?”

Annuity Future Value (Ordinary Annuity):

FV = PMT x [((1 + r)^n - 1) / r]

Where:

  • PMT = annual payment amount
  • r = annual interest rate (as a decimal)
  • n = number of years

This calculates the total accumulated value of making equal annual payments, with each payment earning compound interest for the remaining years. Earlier payments earn more interest because they are invested for a longer period.

The Power of Compound Interest

The key factor in future value is the compounding effect. Interest earns interest over time, creating exponential growth. At 7% annually, money approximately doubles every 10.3 years (using the Rule of 72: 72 / 7 = 10.3). This means $10,000 becomes approximately $20,000 in 10 years, $40,000 in 20 years, and $80,000 in 30 years.

Zero Percent Rate Edge Case

When the interest rate is 0%, the future value simply equals the total contributions. For a lump sum, FV = PV. For an annuity, FV = PMT x n. No interest is earned, so the total is just the sum of all deposits.

Worked Example

For a $10,000 lump sum at 7% for 20 years: FV = $10,000 x (1 + 0.07)^20 = $10,000 x (1.07)^20 = $10,000 x 3.8697 = approximately $38,697. Total contributions = $10,000. Estimated interest earned = $38,697 - $10,000 = approximately $28,697.

For a $5,000/year annuity at 7% for 20 years: FV = $5,000 x [((1.07)^20 - 1) / 0.07] = $5,000 x [(3.8697 - 1) / 0.07] = $5,000 x [2.8697 / 0.07] = $5,000 x 40.9955 = approximately $204,977. Total contributions = $5,000 x 20 = $100,000. Estimated interest earned = $204,977 - $100,000 = approximately $104,977.

Related Calculators

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Estimate simple interest earned or owed on a principal amount over a given time period.

Frequently Asked Questions

What is future value?
Future value is the estimated worth of a current asset or series of payments at a specified date in the future, assuming a certain rate of return. It accounts for compound interest, where earnings on an investment generate their own earnings over time.
What interest rate should I use?
The rate depends on the type of investment. Historically, the US stock market has returned approximately 7% to 10% annually before inflation. Savings accounts and CDs typically offer 1% to 5%. Bonds may return 3% to 6%. Use a rate that reflects the expected return of your specific investment. Lower rates provide more conservative estimates.
What is the difference between lump sum and annuity?
A lump sum is a single, one-time investment made today. An annuity involves making equal payments at regular intervals (annually, in this calculator). Many real-world scenarios combine both, such as opening a retirement account with an initial deposit and then making regular annual contributions.
Does this calculator account for inflation?
Not directly. The result is in nominal (future) dollars. To estimate in today's purchasing power, subtract the expected inflation rate from the interest rate. For example, if the expected return is 7% and inflation is 3%, use 4% to get an inflation-adjusted future value.
How does compounding frequency affect future value?
This calculator assumes annual compounding. More frequent compounding (monthly, daily) produces a slightly higher future value because interest begins earning interest sooner. The difference is relatively small for most practical purposes. For example, $10,000 at 7% for 20 years yields approximately $38,697 with annual compounding and approximately $40,387 with monthly compounding.