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Compound Interest (Periodic)

Also known as compound interest formula

A=P(1+rn)ntA = P \left( 1 + \frac{r}{n} \right)^{n t}

Worked example: $1000 at 6%/yr monthly for 10 yr → A = 1819.40 — press Try an example to run it live, then adjust anything.

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Compound Interest (Periodic) explained

PArnt

With periodic compounding, each period's rate r is split into n slices and applied n times, so past interest starts earning interest of its own. $5,000 at 4% per year compounded monthly (n = 12) for 10 years grows to A = 5000 × (1 + 0.04/12)¹²⁰ ≈ $7,454.16 — about $50 more than yearly compounding would give, because 120 small boosts beat 10 large ones.

Solving for r recovers the rate a savings product actually paid between two statements, and solving for t answers "how long until my balance reaches A?" Enter r as a decimal (4% → 0.04), and note that pushing n toward infinity lands on the continuous-compounding formula A=PertA = Pe^{rt}.

Compound Interest (Periodic) formula

A=P(1+rn)ntA = P \left( 1 + \frac{r}{n} \right)^{n t}
Where
  • AA= Final amount
  • PP= Principal
  • rr= Interest rate per period (decimal)
  • nn= Compounds per period
  • tt= Number of periods

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Part of this formula set

Time value of money

4 formulasSimple interest, periodic and continuous compounding, and discounting a future amount back to what it is worth today.