Compound Interest Calculator
Final amount
1,628.89
Every balance is computed as an exact BigInt fraction — no floating-point rounding.
- Total interest earned
- 628.89
- Effective annual rate exact
- 5%
- Doubling time (years)
- 14.21
Step-by-step solution
- 1
Identify the inputs
With compound interest, each period's earnings are added to the balance, so the next period earns interest on interest. The inputs are listed below.
- P = 1000
- r = 5%
- t = 10
- n = 1
- 2
Convert the annual rate to a fraction
The annual rate 5% becomes the exact fraction 1/20. Every periodic computation below stays in fractions.
- 3
Per-period rate and growth base
With 1 compounding periods per year, each period applies the exact per-period rate i = 1/20. The growth base is B = 1 + i.
- 4
Count the compounding periods
1 periods per year over 10 years gives N = 10 compounding periods in total.
- 5
Grow the principal
The power B^N is expanded exactly with BigInt numerator and denominator — no floating-point rounding — leaving the grown principal at about 1,628.89.
- 6
Total amount
The final amount is the grown principal plus the grown contributions: about 1,628.89.
- 7
Interest earned
Subtracting everything paid in leaves the earnings: about 628.89 of interest on a principal of 1,000.00 and contributions of 0.00.
- 8
Effective annual rate
Compounding more often than once a year beats the nominal rate. The equivalent single yearly growth is EAR = B^n − 1, computed exactly as a fraction — about 5% per year.
- EAR = 1/20 ≈ 5%
- 9
Doubling time
Solving B^(n·t) = 2 with logarithms gives the doubling time: about 14.21 years. The Rule of 72 shortcut, 72 divided by the percent rate, estimates 14.4 years.
- 72 / 5 ≈ 14.4
About compound interest
Compound interest is interest on interest. Instead of being paid out, each period's earnings are added to the balance, so the next period earns interest on a larger amount. With an initial principal P, an annual rate r and n compounding periods per year, the balance after t years is A = P(1 + r/n)^(nt) — the same geometric growth law that drives geometric sequences.
The more often interest is added, the more you earn: monthly compounding beats annual compounding at the same nominal rate, and continuous compounding — the limit as n grows without bound — gives A = P·e^(rt). The effective annual rate (EAR) makes the frequencies comparable: it is the single yearly growth that produces exactly the same balance, EAR = (1 + r/n)^n − 1. A 6% nominal rate compounded monthly is really about 6.17% per year.
Regular contributions turn the formula into an annuity: every payment compounds for the time remaining, and together they grow to C·((1 + r/n)^(nt) − 1)/(r/n) — over long horizons often worth more than the initial principal. For a quick estimate of the doubling time, the Rule of 72 divides 72 by the percent rate: at 5% it predicts about 14.4 years, close to the exact ln(2)/ln(1.05) ≈ 14.21 years.