Compounding Reference

Your figures

Starting amount

Rate

Years

Compounded

GROWS TO

Interest earned

Same at simple interest

Years to double

Try a few — change ONE thing per row

The arithmetic

Compound

P x (1 + r/n) ^ (n x years)

Simple

P x (1 + r x years)

r — DEFINE IT FIRST

the rate as a DECIMAL — 7% is 0.07, not 7

n

compounding periods per year

Doubling time

ln(2) / (n x ln(1 + r/n)), with r as a decimal

Rule of 72

72 / rate — close between about 5% and 12%

Not included

contributions, tax, inflation, fees

What actually moves the answer

1st — Time

the only input that compounds on itself

2nd — Rate

large, and the one people over-estimate

3rd — Starting amount

linear — twice the start is twice the end

Barely — Frequency

annual to daily is a few percent, total

⚠ Inflation

subtract it from the rate for today's money

Before trusting a projection

• Rate justified, not hoped for - use the lower figure if unsure
• Inflation subtracted if you want the answer in today's money
• Tax considered unless the account is sheltered
• Fees subtracted from the rate - a 1% fee is 1% off your return
• Contributions handled separately - this is a lump sum
• Longer timelines re-checked, because errors compound too
• The simple-interest column read as well as the compound one

Time beats rate, and both beat frequency

The single most useful thing this sheet shows is the ORDER. Years matter most because time is the only input that compounds on itself. Rate matters a great deal and is the one people inflate. Compounding frequency is nearly irrelevant — annual to daily is worth a few percent in total, and it is the thing most often advertised.

Optimism compounds too

Assuming 10% instead of 7% roughly doubles a thirty-year projection. That is not a small over-estimate — it is a plan that fails quietly, and late, at the point where there is no time left to correct it. Use a rate you can defend.