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Future Value Calculator

Project how much your money grows over time — 5-way solve, compounding comparison, and milestone tracker.

🎯 Solve For
💰 Starting Amount
$
📈 Growth Factors
%
yrs
💳 Regular Contributions (Optional)
$
PV$10,000 × (1+r/n)1.00583 ^ nt120 + PMT$500/mo = FV—
$0
Future Value in 10 Years

Enter your values above to project future growth.

Total Contributions
$0
Interest Earned
$0
Effective APY
0.00%
Interest % of FV
0%
⏱ Doubling time: —
Year Balance Contributed Interest Growth %
Wealth Breakdown
Principal
Contributions
Interest

Scenario Comparison

Compare two investment scenarios side by side. Adjust each scenario independently, then view results and the combined growth chart.

20 years
Scenario A
$
%
$
Future Value (A)
$0
Scenario B
$
%
$
Future Value (B)
$0
Difference (B − A): $0 (0%)

Growth Over Time

⏰ Power of Starting Earlier (Scenario A)
If you started Scenario A 5 years earlier, you would accumulate an additional $—.

Year-by-Year Projections

Milestone years are highlighted. Based on your Tab 1 inputs.

Year Balance Total Contrib. Interest

Growth with Milestone Lines

Rule of 72
—
Estimate (72 ÷ rate)
Actual 2× Time
—
Simulated years

Years to Reach Multiplier

How to Use This Calculator

1

Enter Present Value

Type in your starting amount — the lump sum you have today (or plan to invest).

2

Set Rate & Time

Enter an annual interest rate and the number of years. Use rate chips to quickly try benchmark returns like S&P 500 (~10%) or HYSA (~4.5%).

3

Pick Compounding Frequency

Choose how often interest compounds: monthly is the most common for savings accounts. Select "Continuous" for the mathematical limit.

4

Add Contributions

Optionally add regular payments (monthly or annual). Toggle "Beginning of Period" if contributions are made at the start of each period (annuity due).

5

Solve Any Variable

Use "Solve For" to find any unknown: the rate needed to hit a goal, the time it takes, or the starting balance you need.

Formulas

FV = PV × (1 + r/n)^(n×t)
FV (with PMT, end) = PV×(1+r/n)^(nt) + PMT×[(1+r/n)^(nt)−1]/(r/n)
FV (annuity due) = FV(end) × (1 + r/n)
FV (continuous) = PV × e^(r×t)
APY = (1 + r/n)^n − 1
Rule of 72: years to double ≈ 72 ÷ r%

Key Terms

Future Value (FV)
The value of a current asset at a future point in time, given an assumed growth rate. The end-goal of this calculation.
Present Value (PV)
The current value of a sum of money. FV and PV are inverses — PV = FV / (1+r/n)^(nt).
Compounding
Earning interest on both the original principal and previously accumulated interest. The frequency (monthly, daily, etc.) determines how quickly interest is reinvested.
APY (Annual Percentage Yield)
The effective annual rate including compounding. APY = (1 + r/n)^n − 1. Always greater than the stated APR when compounding is more frequent than annual.
PMT (Payment)
A regular periodic contribution added to the balance. Monthly contributions dramatically increase future value due to compounding of each payment.
Ordinary Annuity
Contributions made at the end of each compounding period. The standard default for most savings and investment accounts.
Annuity Due
Contributions made at the beginning of each period. Each payment earns one extra compounding period vs ordinary annuity, increasing FV by a factor of (1 + r/n).
Continuous Compounding
The theoretical limit of compounding infinitely often. Uses the formula FV = PV × e^(rt). Yields marginally more than daily compounding in practice.

Examples

Retirement Savings

Starting with $10,000, contributing $500/month, at 7% annually (monthly compounding) over 30 years:

FV ≈ $597,547

Of which $180,000 is contributions and $397,547 is interest — 66% of the final balance is pure compound growth.

College Fund

Saving $200/month for a child born today, at 6% (monthly) over 18 years, starting with $0:

FV ≈ $77,537

$43,200 in contributions and $34,337 in interest. Starting even 2 years earlier adds over $18,000.

Business Goal

You need $100,000 in 5 years. With $20,000 today and no contributions, what annual rate do you need?

Rate ≈ 38% — unrealistic!

Adding $800/month drops the required rate to ~10.5%, achievable via S&P-tracking investments.

How Compounding Frequency Changes Your Outcome

At first glance, the difference between annual and daily compounding seems trivial. But compound frequency interacts with time and contribution size in a nonlinear way that catches most people off guard.

The Math Behind Frequency

The annual percentage yield (APY) for any compounding frequency is: APY = (1 + r/n)^n − 1. At 7% stated rate: annual APY = 7.000%, quarterly = 7.186%, monthly = 7.229%, daily = 7.250%, continuous = 7.251%. The difference between monthly and daily is just 0.02% — nearly negligible for most savers.

When Frequency Matters Most

Frequency has the biggest impact on large lump sums over long periods. A $100,000 lump sum over 30 years at 7%: annual compounding yields $761,226, while daily compounding yields $811,654 — a difference of $50,428. The same $100,000 over 5 years only differs by ~$1,000.

Continuous Compounding as a Limit

Continuous compounding — where interest is added instantaneously — is the theoretical maximum using Euler's number e. The formula FV = PV × e^(rt) gives the same result as compounding n times per year as n → ∞. In practice, no financial product compounds continuously, but it's the standard benchmark in financial mathematics.

The Contribution Timing Effect

Paying at the beginning of each period (annuity due) vs the end (ordinary annuity) might seem like a minor bookkeeping difference. But at $500/month for 30 years at 7%, an annuity due yields approximately $3,500 more — the equivalent of 7 extra monthly contributions, just from timing.

Frequently Asked Questions

What is future value and how is it different from compound interest?

Future value (FV) is the specific end amount your investment grows to. Compound interest describes the mechanism of growth — earning interest on interest. Every compound interest calculation produces a future value as its output. FV is the result; compounding is the process.

How does the FV formula change when I add regular contributions?

Without contributions: FV = PV × (1+r/n)^(nt). With regular payments (ordinary annuity): FV = PV×(1+r/n)^(nt) + PMT×[(1+r/n)^(nt)−1]/(r/n). For annuity due, multiply the PMT term by (1+r/n). The calculator handles all these variants automatically when you enter a contribution amount.

What is continuous compounding and when should I use it?

Continuous compounding uses FV = PV × e^(rt). It's the limit as compounding frequency approaches infinity. Use it for theoretical comparisons or when modeling financial derivatives. For practical savings/investing projections, monthly compounding is typically accurate enough — the difference from continuous is usually under 0.03%.

What does APY mean and why is it different from the interest rate I entered?

The interest rate you enter (r) is the stated annual rate (APR). APY (Annual Percentage Yield) is the effective annual return after accounting for compounding: APY = (1+r/n)^n − 1. At 7% monthly compounding, APY = 7.229%. Banks are legally required to display APY so you can compare products with different compounding schedules fairly.

How do I use Future Value vs Present Value calculators?

Use Future Value when you know what you have today and want to project what it'll grow to. Use Present Value when you know what you'll need in the future and want to know what to invest today. They are mathematical inverses: PV = FV / (1+r/n)^(nt). This calculator's "Solve For: Present Value" mode lets you find PV directly.

How do I find the rate I need to reach a target?

Select "Solve For: Rate" at the top of the calculator and enter your target future value. The calculator uses binary search to find the annual interest rate needed to reach that goal given your current PV, time horizon, and contribution. This is especially useful for reverse-engineering required investment returns.