Simple interest calculates a return only on the initial principal. Compound interest adds each period's return to the balance, so the next calculation uses a larger amount. That difference may look small at first, but it builds over time.
The basic formula
Without recurring contributions, the common formula is:
A = P × (1 + r / n)^(n × t)
A is the final balance, P the initial principal, r the annual rate as a decimal, n the number of compounding periods per year and t the number of years. For example, $1,000 at 5% per year for 10 years with annual compounding would finish near $1,629 before fees and taxes.
What changes with monthly contributions
When you add money regularly, each contribution has a different amount of time to grow. The first contribution is invested for almost the whole term; the last one only participates near the end. Keep these three figures separate:
- Initial principal.
- Total contributions made.
- Interest earned on both amounts.
Compounding frequency also affects the model. Monthly compounding does not turn a poor rate into a good investment, but it can describe more precisely when growth is added to the balance.
Time is often more important than starting big
A simulation helps compare scenarios: starting today or in five years, contributing $100 or $200, or changing the term. It is not a forecast. A constant rate is only an assumption, and real returns can change; fees, taxes and inflation also reduce what reaches your account.
Try several reasonable scenarios and do not mistake a formula for a guarantee. For an educational reference, see the Investor.gov compound interest calculator.