How compound interest works
Compound interest is calculated on the initial principal plus all interest accumulated in previous periods. Unlike simple interest, which only ever applies to the original amount, compound interest means your gains start generating their own gains — the classic "interest on interest" effect.
Where P is the initial principal, r is the annual rate as a decimal, n is the number of compounding periods per year, t is time in years, and PMT is the contribution made at each period.
Why compounding frequency matters
For the same nominal annual rate, compounding more often (daily or monthly instead of annually) produces a slightly higher effective return, because each smaller period's interest starts earning interest sooner. The difference is usually modest over short periods but becomes more noticeable over many years.
The effect of recurring contributions
Adding a fixed contribution at every compounding period — the classic "dollar-cost averaging" approach used in retirement accounts and index fund investing — can grow a balance far faster than a single lump sum left alone, especially over long time horizons, because each new contribution also gets the benefit of compounding for the periods that follow it.
Common uses
- Retirement planning: projecting how monthly contributions to an investment account grow over decades.
- Savings goals: comparing how different interest rates or compounding frequencies affect a target balance.
- Debt awareness: the same formula explains how compounding works against you on credit card balances.
Frequently asked questions
Does this calculator account for taxes or inflation?
No — it projects nominal growth based on the rate you enter. To estimate real (inflation-adjusted) growth, use an interest rate reduced by your expected inflation rate. Taxes on gains vary too much by country and account type to build into a generic formula.
Can I use this for a loan instead of an investment?
The same compounding math applies, but loan payments are usually structured differently (amortized, with payments reducing principal). For loan-specific calculations, the Auto Loan Calculator is a better fit.
How does compound interest work?
You earn interest on your balance and on the interest already added, so growth speeds up over time. A = P(1 + r/n)^(nt).
What is the difference between simple and compound interest?
Simple interest is only on the original amount; compound interest is on the amount plus accumulated interest, which is why it grows faster.
How often should interest compound?
More often is better for the saver — daily beats monthly beats yearly — though the difference is small unless the rate or time is large.