How does periodic contribution compound growth work?

Compound growth with regular contributions combines two components: the exponential growth of the starting principal (FV = P * (1 + r/n)^(n*t)) and the accumulated growth of periodic deposits via the future value of an annuity formula (FV = PMT * [((1 + r/n)^(n*t) - 1) / (r/n)] * timing multiplier).

What is the difference between beginning (Annuity Due) and end (Ordinary Annuity) contribution timing?

When contributions are made at the beginning of each period (Annuity Due), each deposit earns an additional period of compound interest compared to deposits made at the end of each period (Ordinary Annuity). Over a 10 to 30 year horizon, beginning-of-period deposits generate noticeably higher compounding yields.

What is the difference between 365 calendar days and 260 trading days for daily compounding?

The 365-day basis is standard for bank high-yield savings accounts and daily interest accrual across all calendar days. The 260-day basis represents standard trading and business days (52 weeks x 5 days/week), which is commonly used when modeling automated daily stock purchases or payroll deposits.

What is a market variance band?

A variance band creates an upper and lower envelope around your expected annual return (e.g. 7% +/- 2% creates a 5% to 9% range). This allows investors to plan for realistic market volatility rather than assuming a rigid, static rate of return.

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WealthLyra

Compound Growth Pro

Advanced projection modeling with variance band confidence intervals & contribution frequency comparison engines.

Investment Parameters

Initial Starting Principal

Regular Contribution Amount

Contribution Frequency

Daily Basis Day-count convention

Contribution Timing

Time Horizon (Years)

Expected Return

Variance Band (+/-)

Expected Balance

After 15 years

Total Principal

Your contributions

Interest Earned

Compound yield

Portfolio Trajectory & Variance Band

Frequency Comparison Matrix

Final balance if the same annual capital ($0/yr) is deposited at different contribution frequencies.

Mathematical Framework

How Compound Growth Pro Calculates Your Wealth

Unlike simplified calculators that only compound once per year, Compound Growth Pro utilizes periodic compounding formulas synchronized to your contribution schedule and day-count convention.

1. Periodic Compounding Formula

Starting principal grows via P × (1 + r/n)^(n×t). Regular contributions grow as an annuity series with an exact multiplier for beginning of period (Annuity Due) vs end of period (Ordinary Annuity).

2. Confidence Variance Modeling

Markets never produce a fixed, identical return year after year. The variance band calculates optimistic and conservative trajectory envelopes (r ± v) so you can plan for real-world market volatility.

Frequently Asked Questions

Why does contribution timing matter?

Making deposits at the start of each month/period allows that cash to compound for the full duration of that period. Over decades, starting at the beginning of each cycle rather than the end can add tens of thousands in compound yield.

When should I use 365 vs 260 days?

Select 365 Days when modeling high-yield savings accounts, money market funds, or daily bank interest. Select 260 Days when modeling daily dollar-cost averaging into stock markets (52 weeks × 5 business days).

Are my financial numbers stored or sent anywhere?

Never. WealthLyra operates completely client-side in your local web browser. No figures, portfolio balances, or private inputs ever touch an external server or third-party tracking network.

How is total interest calculated?

Total compound yield is calculated by subtracting your cumulative invested capital (Principal + all periodic deposits) from the final projected portfolio balance.