How Your Savings Grow with Compound Interest
The compound interest formula is: A = P(1 + r/n)^(nt) + PMT × ((1 + r/n)^(nt) − 1) / (r/n), where P is the initial deposit, r is the annual interest rate, n is compounding periods per year, t is years, and PMT is the monthly contribution.
The most powerful factor in savings is time. $5,000 invested at 7% for 40 years grows to $74,872 — even with no additional contributions. Add $200/month and the final balance reaches $560,000. Starting 10 years earlier can more than double your final balance.
The second most important factor is the interest rate. Even small differences compound significantly over decades. Going from 5% to 7% over 30 years more than doubles your ending balance on the same contributions.
Rule of 72
Divide 72 by your annual interest rate to estimate how many years it takes to double your money. At 6%: 72 ÷ 6 = 12 years to double. At 8%: 72 ÷ 8 = 9 years.
Frequently Asked Questions
What is the difference between compound and simple interest?+
Simple interest is calculated only on the principal. Compound interest is calculated on the principal PLUS accumulated interest. Over time, this difference is enormous. $10,000 at 6% simple interest for 30 years = $28,000. At 6% compound (annual) = $57,435 — more than double.
How often should interest compound?+
The more frequently interest compounds, the faster your money grows. Daily compounding grows slightly faster than monthly, which grows faster than annual. The difference between daily and monthly is small, but annual vs monthly can matter significantly over long periods.
What is a realistic interest rate for savings?+
High-yield savings accounts currently offer 4–5% (2025 rates). Index fund ETFs historically average 7–10% annually over long periods. Bonds offer lower returns with lower risk. Your savings strategy should match your time horizon and risk tolerance.
How do I maximize my savings?+
Start early (time is the most powerful factor), contribute consistently, reinvest all interest and dividends, minimize fees, increase contributions whenever income rises, and take full advantage of tax-advantaged accounts (401k, IRA, HSA).