Compounding frequency
Compounding frequency is how many times per year interest is calculated and added to a principal balance. More frequent compounding means interest earns interest sooner, raising the true annual return above the stated nominal rate.
FrameworkTime value of money
See it move
€1,000 invested at a 6% nominal rate for one year grows to €1,060.00 with annual compounding. Compounded monthly instead — twelve times over the same year, at one-twelfth the rate each time — the same €1,000 and the same nominal 6% grow to €1,061.68. The gap is small over one year but widens over longer horizons, so frequency matters as much as the stated rate.
The formula
Variables
- Future value after t years
- Present value (initial principal)
- Nominal annual interest rate (as a decimal)
- Number of compounding periods per year
- Time in years
At the limit of continuous compounding (m → ∞): FV = PV × e^(r × t). Increasing m raises FV for the same nominal rate, explaining why the effective annual rate always exceeds the nominal rate when compounding is more frequent than annual.
Check yourself
A deposit of €10,000 is made for five years at a nominal annual interest rate of 5%. All other conditions are identical. Which compounding arrangement produces the highest terminal value at maturity?