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💰 Compound Wealth Builder

Model how an initial deposit plus monthly contributions compound into long-term wealth. Adjust the return rate and time horizon to see contributions versus growth split apart.

Financial Models & Markets3DEasy60 FPS

The Compounding Formula

Future value with regular contributions: FV = P·(1+r)ⁿ + PMT·(((1+r)ⁿ − 1)/r), where P is the initial investment, PMT is the monthly contribution, r is the monthly rate (annual rate ÷ 12) and n is the number of months (years × 12). The first term is your lump sum growing on its own; the second term is the snowballing value of every monthly deposit compounding for the months it has left to grow.

Contributions vs Growth

The teal line tracks money you actually paid in — principal plus the running sum of monthly contributions. The gold line tracks the total account value. The shaded gap between them is pure compounding: interest earned on interest, month after month, without you lifting a finger. Over long horizons that gap usually ends up larger than everything you deposited.

Rule of 72 & Time Horizon

A quick mental shortcut: divide 72 by the annual return percentage to estimate the years needed to double your money. At 7% that's roughly 10.3 years; at 12% it's about 6 years. Because compounding is exponential, the last decade of a long investment horizon typically contributes more growth than all the earlier decades combined — which is why starting early matters more than the size of any single deposit.

About this simulation

This simulation models compound growth with regular contributions: an initial investment P grows monthly at rate r = annual return ÷ 12, while a monthly contribution PMT is added at the end of every month and starts compounding from that point on. The result, FV = P·(1+r)ⁿ + PMT·(((1+r)ⁿ−1)/r), is exactly the formula banks and pension calculators use for a fixed-rate savings or investment account.

🔬 What it shows

Two lines climbing over time — a teal line for total contributions (initial deposit plus every monthly payment added up) and a gold line for total account value including compounding growth. The gold line always sits at or above the teal line, and the shaded teal band between them is money you never deposited: interest earned on interest.

🎮 How to use

Drag the Initial investment and Monthly contribution sliders to set how much you put in. Move Annual return to test different growth assumptions (a savings account, a bond fund, or a stock index), and drag Years to see how the shape of the gap between the two lines changes over short versus long horizons. The stats panel updates live with the final value, total contributed, total growth, and growth's share of the final pot.

💡 Did you know?

At a 7% annual return, doubling your time horizon from 20 to 40 years doesn't just double your final value — because growth compounds on itself, it can multiply it four times over or more, depending on how much you contribute monthly. That's why starting early is consistently rated the single biggest lever in long-term investing, ahead of chasing a slightly higher return.

Frequently asked questions

What's the difference between the teal line and the gold line?

The teal line is simply the money you put in — your initial investment plus every monthly contribution added up, with no growth applied. The gold line is the actual account balance, which includes compounding interest on top of those contributions. The shaded gap between them is growth you didn't deposit yourself; it's the return the market or bank paid you for letting your money sit and compound.

Why does monthly compounding matter instead of just annual compounding?

With monthly compounding, interest is calculated and added to your balance twelve times a year instead of once, so each month's interest is itself immediately eligible to earn more interest. Over many years this produces a slightly higher final value than annual compounding at the same quoted rate, because the "principal" that earns interest grows more often.

How do I use the Rule of 72 with this simulator?

Divide 72 by the Annual return percentage to estimate how many years it takes an amount to double, ignoring further contributions. At 6% that's about 12 years; at 9% about 8 years. Set the Years slider to that number with Monthly contribution at £0 and check that the Final value in the stats panel is roughly double your Initial investment — a good sanity check on the underlying formula.

Why does total growth eventually exceed total contributions?

Because compounding is exponential while contributions only accumulate in a straight line. Early on, most of the account balance is money you deposited. But each pound of growth also starts earning its own growth, so given enough years the compounding curve overtakes the straight contribution line — often decisively, which is exactly what the widening gap between the two lines on the chart shows.

Is this simulator giving investment advice?

No. It is a plain mathematical model of compound interest with fixed assumptions — a constant annual return, no fees, no taxes, and no market volatility. Real investments fluctuate year to year and carry risk and costs that this simplified model doesn't include. Use it to build intuition about compounding, not as a forecast of any specific investment's future performance.

⚙ Under the hood

Model how a lump sum plus monthly contributions compound monthly at a chosen annual return. Watch the gap between money you put in and money growth adds widen over the years.

Three.jsCompound InterestPersonal FinanceInvesting

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install