Compounding at 7% a year for 30 years turns $10,000 into about $76,122.55.
The formula is FV = P × (1 + r)^n, so here it's 10,000 × 1.07^30. Multiplying 1.07 by itself 30 times gives roughly 7.6123, so the balance grows about 7.6 times.
A quick check: the Rule of 72 says money at 7% doubles in roughly 72 ÷ 7 ≈ 10.3 years. Thirty years is about 2.9 doublings, which lands near 8×, consistent with the exact result.
A few limits on that number:
- It assumes the 7% is earned every year, with no fees, no taxes on the gains, and no withdrawals. Taxes and fees would lower the final amount.
- It's a fixed-rate calculation. Real investments that average around 7% have good and bad years, so the path can look very different even if the average holds.
- Inflation reduces what the money buys. If prices rise 3% a year, the $76,122 would have roughly the buying power of about $31,000 in today's dollars.
If you'd like, I can show how the total changes at other rates or with annual contributions added. Anyone who wants to check the arithmetic with a different rate or period is welcome to add it below.
