2026-09-21 7 min read

Savings Growth Calculator

Year-by-year balance, deposits and interest for any savings rhythm.

Calculator

Initial Deposit Help

Lump sum you start with today.

Contribution Each Period Help

Added at the end of each compounding period.

Annual Interest Rate (nominal)(%)

Time Horizon(years)

years

Extra Months(months)

months

Compounding Frequency

This savings goals calculator compounds monthly (12) at the nominal rate you enter, with contributions added at the end of each period. Compare accounts on APY — it already includes compounding.

Year-by-year growth

Balance, contributions and interest credited each year.

Year	Balance	Contributed	Interest
1	$12,967	$12,400	$567
2	$16,087	$14,800	$1,287
3	$19,365	$17,200	$2,165
4	$22,812	$19,600	$3,212
5	$26,435	$22,000	$4,435
6	$30,243	$24,400	$5,843
7	$34,246	$26,800	$7,446
8	$38,454	$29,200	$9,254
9	$42,877	$31,600	$11,277
10	$47,527	$34,000	$13,527

Results

Optimal

Projected balance

$47,527

Projected balance after 10 years.

Total contributions

$34,000

Total interest earned

$13,527

Effective annual yield (APY)

5.12%

Live results update as you type — currently showing projected balance of $47,527 over 10 years. Replace the defaults with your own figures for an exact plan.

Visualizations

Interest earned each year

567$Y1

719$Y2

879$Y3

1,047$Y4

1,223$Y5

1,408$Y6

1,603$Y7

1,808$Y8

2,023$Y9

2,249$Y10

What makes up the final balance

Initial deposit21%

Contributions50%

Interest earned28%

Balance growth over time

Formula

Growth, doubling and rules share one core: exponential compounding. The exact doubling time inverts the compound formula with logarithms; the rules approximate it for mental math.

FV = P × (1 + r/n)^(n×t) · t₂ = ln 2 ÷ (n × ln(1 + r/n)) · t ≈ 72 ÷ r

Variables

Symbol	Name	Unit	Description
P	Starting balance	$	Lump sum left to grow
r	Annual rate	%	Nominal yearly rate
t₂	Doubling time	years	Years for the balance to double

Explanation

The growth figure shows compounding speed; the doubling time turns an abstract rate into calendar years you can feel.

Step-by-Step Calculation

Follow each step to understand how the result is calculated from your inputs.

Step 1

Periodic rate: 5% ÷ 12 compounding periods

i = r ÷ n

Result: i = 0.004167 per period

Step 2

Number of periods: 12 × 10.00 years

N = n × t

Result: N = 120 periods

Step 3

Grow the initial deposit with compound interest

P × (1 + i)^N

Result: $10,000.00 → $16,470.09

Step 4

Grow the stream of contributions (ordinary annuity)

PMT × (((1 + i)^N − 1) ÷ i)

Result: Contributions grow to $31,056.46

Step 5

Add both parts for the headline balance

Result: Future value = $47,527

Final Answer

$47,527

Worked Examples

See how the calculator works with different scenarios.

Scenario

The savings growth calculator run on the values above, showing the full calculation path rather than only the answer.

Inputs

Principal:10000

Contribution:200

Rate:5

Years:10

Calculation

1. Periodic rate: 5% ÷ 12 compounding periods → i = 0.004167 per period 2. Number of periods: 12 × 10.00 years → N = 120 periods 3. Grow the initial deposit with compound interest → $10,000.00 → $16,470.09 4. Grow the stream of contributions (ordinary annuity) → Contributions grow to $31,056.46 5. Add both parts for the headline balance → Future value = $47,527

Result

Projected balance: $47,527

Interpretation

Compounding frequency matters less than rate and time: moving from annual to monthly compounding at 5.00% lifts the effective yield to 5.12%. Automate the $200 monthly contribution — consistency beats timing.

Understanding Your Result

Your Result: Projected balance: $47,527

Typical range: At 5.00% compounded monthly (12), interest contributes 28.5% of the final balance over 10 years.

What This Means

The growth figure shows compounding speed; the doubling time turns an abstract rate into calendar years you can feel.

Why It Matters

Professional Interpretation

How this is calculated

Growth, doubling and rules share one core: exponential compounding. The exact doubling time inverts the compound formula with logarithms; the rules approximate it for mental math.

What drives the result

Exact doubling time comes from t = ln2 ÷ (n×ln(1+r/n)); the Rules of 72 and 69.3 approximate it as constant ÷ rate. CAGR reverses the lens: the smooth annual rate that connects a start and end balance.

Recommendations

•Keep the $200 contribution automatic; missed periods cost more than a slightly higher rate elsewhere.
•Compare accounts on APY (5.12% here), not the nominal rate — APY already includes compounding.
•Extend the horizon before chasing yield: an extra 5 years at 5.00% usually beats +1 point of rate.

Educational Content

Introduction

Growth math answers “how fast?” — the doubling time, the Rule of 72 shortcut, and the compound annual growth rate behind any balance trajectory.

Concept Explanation

Applications

▸Sanity-checking return claims

▸Mental-math doubling estimates

▸Smoothing lumpy growth into one rate

Benefits

•Makes exponential growth intuitive
•Catches unrealistic promises fast
•Works for savings, investments and prices

Limitations

•Rules are approximations tuned for 4–12% rates
•CAGR hides volatility — the ride may be bumpier than the average

Best Practices

•Use exact doubling time for plans, rules for conversation
•Pair CAGR with the time horizon — the same gain over fewer years is a higher rate

Common Misconceptions

Myth: The Rule of 72 is exact

Truth: It is within ~0.2 years for typical rates — good enough for decisions, not for contracts.

Myth: Doubling twice means 4× in double the time

Truth: Correct — and that is exactly why early years matter most.

Practical Tips

•Count doublings inside your horizon: each doubling is a 2× on everything saved so far.

Common Mistakes

Applying doubling time to a contribution stream

Doubling formulas assume a lump sum left alone — contributions shorten the effective wait.

Assumptions

This calculator makes the following assumptions to provide estimates:

Untouched lump sum: No deposits or withdrawals during the doubling wait.

Limitations

Be aware of these limitations when using this calculator:

Limitation: Rules are approximations tuned for 4–12% rates

Limitation: CAGR hides volatility — the ride may be bumpier than the average

Frequently Asked Questions

Answers to common questions about this calculator.

When is the Rule of 72 good enough?

For rates 4–12% it lands within ~0.2 years — fine for decisions, not contracts.

Who uses the savings growth calculator?

It is used by savers planning deposits, by advisers comparing account yields, and by households pacing a savings to a deadline. It sits in the Savings Goals group of the Compound Interest & Savings section of Atlascalcs.

How accurate is the savings growth calculator?

Every figure follows directly from the inputs using standard compounding mathematics, so it is accurate to the quality of the values you enter. Banks round interest and apply their own day-count and crediting rules, so expect small differences against a formal statement or maturity advice.

Do these calculators include taxes and inflation?

No — figures are before tax and in nominal terms. For a real-terms view, subtract your marginal tax drag and expected inflation from the rate before entering it.

Why does compounding frequency barely change my result?

Because at typical savings rates the periodic rate is tiny; frequency moves APY by hundredths of a point. Rate and time dominate — automate contributions and protect the horizon.

Related Calculators

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Related Guides

Deepen your understanding with these educational resources.

Compound interest and APY guide

Nominal vs effective rates, compounding frequency and how to compare accounts.

Savings goals that actually get funded

Turning targets into automated monthly numbers with sinking funds.

CDs and ladders explained

When to lock a rate, when to ladder, and what early withdrawal really costs.

Glossary

Technical terms used in mortgage calculations explained in plain language.

Doubling time: Years for a lump sum to double; exact via logarithms, approximated by 72 ÷ rate.
Compounding: Earning interest on previously earned interest; frequency is how many times a year it happens.
APY (annual percentage yield): The realised yearly yield after compounding — the honest way to compare deposit accounts.

Authoritative References

Trusted sources and standards referenced by this calculator.

FDIC — Deposit insurance and savings account basics Consumer Financial Protection Bureau — Savings accounts Federal Reserve — Consumer credit and savings data (G.19) IRS — Interest income (Topic 403) U.S. Treasury — TreasuryDirect savings bonds

Applicable Standards

Discrete end-of-period compounding; contributions credited after that period’s interestAPY computed as (1 + nominal/n)^n − 1 on the quoted nominal rateMoney rounded for display only; all calculations run at full precisionDeposit figures before tax and inflation unless you enter a net rate

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Page Information

Last Updated:

2026-09-21

Version:

2.0.0

References:

License:

Free to use for educational and professional purposes.