How compound interest works
Compound interest means each interest period can earn interest on the balance already accumulated. With recurring deposits, the exact result depends not only on the rate and time period but also on when deposits are added and how the stated annual rate compounds.
Formula
A = P(1 + r/n)^(nt)For a single starting deposit, A is the final amount, P is the starting principal, r is the nominal annual rate as a decimal, n is the number of compounding periods per year, and t is time in years.
Recurring monthly contributions need more than the basic single-deposit formula. BQ Calculator converts the selected nominal compounding schedule to an equivalent monthly rate and simulates each month, adding the contribution before or after interest according to your timing selection.
Algorithm used by this calculator
effectiveAnnualRate = (1 + r/n)^n - 1
monthlyRate = (1 + effectiveAnnualRate)^(1/12) - 1The calculator then iterates month by month without rounding intermediate balances. Display rounding is applied only after the calculation.
Worked example
With a $5,000 starting balance, $300 contributed at the end of each month, a 5% nominal annual rate compounded monthly, and a 10-year period, the calculator applies the equivalent monthly rate to each monthly balance. Change any field above to see the full projection update instantly.
Assumptions and limitations
This model assumes a constant rate, equal monthly deposits, no withdrawals, and no taxes, fees or market volatility. It is a planning tool, not financial advice or a promise of future returns.
Frequently asked questions
What is compound interest?
Compound interest is interest earned on both the original principal and previously accumulated interest. As the balance grows, the amount of interest earned in later periods can grow too.
How often should interest compound?
More frequent compounding produces a slightly higher effective annual yield when the nominal annual rate is the same. The practical difference can be small at ordinary rates, but the calculator lets you compare annual, quarterly, monthly and daily compounding.
Does monthly contribution timing matter?
Yes. A contribution made at the beginning of a month has an extra month to earn interest compared with the same contribution made at the end of the month.
What is the difference between APR and APY?
APR is commonly expressed as a nominal annual rate, while APY reflects the effect of compounding over a year. This calculator derives an effective annual yield from the nominal rate and compounding frequency you select.
Can this calculator predict investment returns?
No. It models a constant rate and regular contributions. Real investment returns vary, fees and taxes may apply, and past performance does not guarantee future results.