The compound interest formula
Compound interest means you earn interest on your interest, not just on your original deposit. The formula for a single lump-sum deposit is:
A = P × (1 + r/n)n×t
- A the final amount after growth
- P your principal (starting amount)
- r the annual interest rate, as a decimal (7% = 0.07)
- n how many times per year interest compounds (12 for monthly, 365 for daily, 1 for annually)
- t the number of years
Worked example: does compounding frequency actually matter?
Take $1,000 at a 7% annual rate for 10 years, and compare compounding annually, monthly, and daily:
Annually (n=1): 1,000 × (1.07)10 = $1,967.15
Monthly (n=12): 1,000 × (1 + 0.07/12)120 = $2,009.66
Daily (n=365): 1,000 × (1 + 0.07/365)3650 = $2,013.62
Switching from annual to monthly compounding gains you about $42.51 over 10 years on a $1,000 deposit. Going from monthly all the way to daily only adds another $3.96 on top of that. Compounding frequency matters, but nowhere near as much as the interest rate itself or how long you leave the money invested.
Adding regular contributions
Most real savings plans aren't a single lump sum they add a fixed amount every period. Each contribution starts compounding from the moment it's added, so contributing consistently matters more than most people expect. Take a $1,000 starting balance, adding $100 every month, at 7% compounded monthly, for 10 years:
Final balance: $19,419.11
Total contributed (principal + deposits): $1,000 + ($100 × 120) = $13,000.00
Growth from interest alone: $6,419.11
Almost a third of that final balance money you never actually deposited came purely from compounding.
Compound Interest Calculator → plug in your own starting amount, contributions, and rate to see it grow instantly.Why starting early beats contributing more
Here's the example that surprises people most. Compare two savers, both earning 7% a year, compounded annually, both retiring at 65:
Saver A invests $5,000/year from age 25 to 35 (10 years), then stops completely and lets it sit untouched for 30 more years.
Saver B invests $5,000/year from age 35 to 65 (30 years) three times as long.
Saver A contributes $50,000 total. Saver B contributes $150,000 total three times more. Yet at age 65:
Saver A's balance: $525,871.63
Saver B's balance: $472,303.93
Saver A ends up with more money despite contributing a third as much, purely because their money had 10 extra years to compound. Time in the market is doing more work here than the size of the contributions which is the entire case for starting to save as early as possible, even in small amounts.