The compound interest formula
For a starting principal P, periodic contribution C, annual rate r, n compounding periods per year, and t years:
FV = P(1 + r/n)nt + C × [((1 + r/n)nt − 1) ÷ (r/n)]
The first term is the future value of the starting principal. The second is the future value of an annuity — the sum of all your contributions plus the interest each contribution has earned. Note: this assumes contributions occur at the end of each compounding period (ordinary annuity).
Why compounding frequency matters less than people think
Going from annual to monthly to daily compounding only adds a small amount at typical interest rates. At 7% annual, $10,000 over 30 years grows to roughly $76,123 compounded annually vs $80,919 compounded daily — about a 6% difference. The driver of long-run wealth is rate × time, not compounding frequency.
Real vs nominal returns
The "real" value is your future balance adjusted for inflation — what it would buy in today's dollars. With 3% inflation, $100,000 thirty years from now has the purchasing power of roughly $41,000 today. Always think in real terms for long-horizon planning.