ComputeYard

The math, explained — built by a derivatives quant.

Compound Interest Calculator

See how an initial investment grows over time as interest compounds on itself — with optional regular contributions and your choice of compounding frequency.

How it works

Compound interest is interest earned on both your original principal and on the interest already credited. The more often it compounds — annually, semi-annually, quarterly or monthly — the faster the balance grows, because each period's interest starts earning its own interest sooner.

The calculator uses the exact closed-form future-value formula rather than looping period by period, so there is no rounding drift. The period rate is the annual rate divided by the number of compounds per year, and the number of periods is that frequency times the number of years. Regular contributions are added each period; choose whether they land at the end of each period (an ordinary annuity) or the start (an annuity-due, where every contribution earns one extra period of growth). A year-by-year schedule shows the running balance, contributions and interest.

Worked example

Invest $1,000 at an 8% annual rate compounded quarterly for 1 year, with no contributions:

  • Period rate i = 8% / 4 = 2%; periods = 4 × 1 = 4.
  • Future value = $1,000 × 1.024 = $1,000 × 1.08243216 = $1,082.43.
  • Total contributions = $1,000; total interest = $82.43.

Compounded only once a year at the same 8% the balance would be exactly $1,080 — the extra $2.43 is the benefit of compounding four times instead of one.

The formula

i = annual_rate / compounds_per_year      periods = compounds_per_year × years
FV_principal = principal × (1 + i)^periods
FV_contrib   = contribution × ((1 + i)^periods − 1) / i      (i ≠ 0)
             = contribution × periods                        (i = 0)
if timing = begin:  FV_contrib ×= (1 + i)
future_value        = FV_principal + FV_contrib
total_contributions = principal + contribution × periods
total_interest      = future_value − total_contributions

FAQ

How does compounding frequency affect the result?
More frequent compounding (monthly vs annually) credits interest sooner, so it starts earning its own interest sooner and the final balance is slightly higher for the same annual rate.
Can I include regular contributions?
Yes — set a per-period contribution and choose whether it is added at the end or the start of each period. Start-of-period contributions (an annuity-due) earn one extra period of growth.
Is the math exact?
It uses the closed-form future-value formula with exact decimal arithmetic, so the year-by-year schedule reconciles exactly with the final future value — there is no period-by-period rounding drift.

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