Compound Interest Calculator

Compound interest is interest earned on interest: each period's return joins the balance and earns its own return in the next. This calculator projects that snowball directly — it simulates your balance month by month over up to 100 years, adds your monthly contribution, and reports the final balance, everything you put in, and the interest the process generated.

How It Works

Rather than evaluating a single closed-form formula, the tool runs a monthly simulation:

Your chosen compounding frequency is converted into an effective monthly rate. For monthly compounding that is simply the annual rate divided by 12. For daily, quarterly, semi-annual or annual compounding, the tool first converts the nominal rate to an effective annual rate, then takes the equivalent monthly rate, so contributions deposited monthly are compounded consistently.
Each month, the balance is multiplied by one plus the effective monthly rate — interest is applied — and then your monthly contribution is added at the end of the month.
After the final month, the tool totals your contributions (initial balance plus all deposits) and reports the difference between the final balance and your contributions as total interest, with a year-by-year breakdown.

Because contributions land at month-end, a deposit starts earning interest from the following month.

The Formula

For a single lump sum with no contributions, the simulation matches the classic formula:

$A = P \left(1 + \frac{r}{n}\right)^{nt}$

where $P$ is the principal, $r$ the annual rate as a decimal, $n$ the compounding periods per year, and $t$ the years. With monthly contributions, the simulation applies the same growth monthly and adds each deposit after interest — equivalent to adding the future value of an ordinary annuity:

$A = P(1 + i)^{N} + PMT \times \frac{(1 + i)^{N} - 1}{i}$

with $i$ the effective monthly rate and $N$ the total months. The interest is then simply the final balance minus everything you contributed.

Input Parameters

| Parameter | Unit | Description | |---|---|---| | Initial Balance | Currency | The starting principal; can be zero. | | Monthly Contribution | Currency | Deposited at the end of every month. | | Duration | Years | Horizon from 1 to 100 years. | | Interest Rate | % per year | The assumed constant annual return. | | Compounding Frequency | Choice | Daily, monthly, quarterly, semi-annually or annually. |

Worked Example

Start with $10,000, add$ 500 a month for 10 years at a 7% annual rate, compounded monthly.

Monthly rate: 7% ÷ 12 = 0.5833%.
After 120 simulated months, the final balance is $106,639.02.
Your contributions: $10,000 initial plus$ 500 × 120 = $60,000, totaling **$ 70,000**.
Interest earned: $106,639.02 −$ 70,000 = $36,639.02 — more than a third of the final balance came from compounding, not deposits.

Compounding frequency matters, but less than most people expect: the same inputs compounded annually finish at $105,197.38**, while daily compounding reaches **$ 106,772.85. The gap between annual and daily is real money on large balances, yet it is dwarfed by the effect of the rate or the horizon — extending this plan by five years adds far more than any frequency change.

Interpreting the Results

The interest share grows with time. Early on, growth is mostly your deposits. Later, interest on the accumulated balance overtakes them — that crossover is the snowball effect, and it is why starting early beats contributing more later.
Total contributions is your own money back — the honest baseline. Judge any projection by how much of the final balance is interest rather than deposits.
The annual breakdown shows the balance, cumulative contributions and cumulative interest at each year-end, making the acceleration visible: in the example, year 10 alone adds more interest than the first three years combined.

Compound vs Simple Interest

Simple interest is charged only on the original principal: $10,000 at 7% simple for 10 years earns a flat$ 7,000. Compounding the same principal monthly — with no contributions — earns about $10,096 over the same decade, because each month's interest itself earns interest thereafter. The gap widens with time and rate: over 30 years the compounded principal roughly octuples while the simple-interest balance merely triples. Debt works the same way in reverse, which is why credit-card balances snowball against borrowers.

Limitations

Constant rate. Real returns vary year to year; a smooth 7% is a planning assumption, not a forecast. Variable returns change the result, especially early losses.
No taxes or fees. Interest and gains are shown gross. Tax on investment income and fund fees both drag on real compounding.
Nominal dollars. The projection is not adjusted for inflation. At 3% inflation, a balance 20 years out buys roughly 45% less than its face value suggests.

Frequently Asked Questions

Does compounding frequency really matter?

Modestly. On the worked example, daily compounding beats annual compounding by about $1,575 on a$ 107,000 balance — worth having, but the contribution amount, the rate and the horizon each move the result far more.

Why do my contributions not earn interest in their first month?

The simulation deposits each contribution at the end of the month, after that month's interest is applied — the standard ordinary-annuity convention. A beginning-of-month convention would produce a slightly higher balance.

What return should I assume for investments?

The calculator accepts anything from 0% to 1,000%, but sensible planning uses modest figures: savings accounts near current deposit rates, and long-run diversified portfolios often modeled at 5–8% before inflation. Higher assumed returns compound small optimism into large errors over decades.

Compound Interest Calculator