The doubling penny
One cent, doubled every day for 30 days.
Day 30
$5,368,709.12
Compound interest calculatorSee what your money becomes.
Time does the heavy lifting. Change a number and watch it grow.
Final balance $0
Contributed$0
Interest earned$0
| Year | Contributed (yr) | Interest (yr) | Total contributed | Total interest | Balance |
|---|
Compounding is Amazing
Here are two incredible illustrations.
Folding paper
Fold a sheet of paper 42 times…
440,000 km
…and it reaches past the Moon. Each fold doubles the thickness: 0.1 mm becomes a hand, a football field, two Burj Khalifas — then 440,000 km, beyond the Moon at 384,400 km.
Start early vs. start late
Same finish. One third the effort.
Ana saves for 10 years and stops. Ben saves the same amount for 30 years. Both retire at 65.
Invests 10 years
Ana · ages 25–35, then stops
- Put in
At 65
Invests 30 years
Ben · ages 35–65
- Put in
At 65
Fee drag
Small percentages, large differences.
$10,000 plus $500/month for 30 years at 7% before fees, compounded monthly.
The math
How it's calculated
With a monthly rate i, an initial amount P, a monthly contribution C and N months:
FV = P(1 + i)N + C · [(1 + i)N − 1] / i
For monthly compounding, i = r / 12. For annual or daily compounding we use the equivalent monthly rate i = (1 + r/n)n/12 − 1, so the balance at each year-end matches compounding n times a year exactly.
Assumptions
- Contributions are made at the end of each month.
- The yearly increase raises the monthly contribution once per year, starting in year 2.
- The rate is constant; no taxes. Today's-dollar figures divide by (1 + inflation)years.
- Fees are subtracted from the annual return.
FAQ
Common questions
What is the compound interest formula?
For a lump sum, A = P(1 + r/n)nt: principal P, annual rate r, n compounding periods per year, t years. With monthly contributions C, add C · [(1 + i)N − 1] / i, where i is the monthly rate and N the number of months.
What is the difference between APR and APY?
APR is the stated yearly rate before compounding. APY is what you actually earn in a year once interest compounds: APY = (1 + APR/n)n − 1. A 7% APR compounded monthly is about 7.23% APY.
How does monthly compounding work?
Each month, interest of r/12 is added to the balance, and next month’s interest is earned on that larger balance. At 7%, that is about 0.583% a month.
What is the Rule of 72?
Divide 72 by the annual rate to estimate how many years it takes money to double. At 7%, 72 ÷ 7 ≈ 10.3 years; the exact figure is about 10.2 years. It is most accurate for rates between roughly 6% and 10%.