How the calculation works
Equivalent interest rates describe the same accumulation
Interest rates can be quoted in several mathematically equivalent forms. An 8% effective annual interest rate is not the same number as a nominal annual rate compounded monthly, but there is a monthly-compounded nominal rate that produces exactly the same one-year growth.
This calculator first converts the source rate to an effective annual interest rate. It then derives equivalent nominal, periodic, discount, and force-of-interest values from that common basis.
i is the effective annual interest rate, j the nominal annual rate, m periods per year, d the effective discount rate, and δ the force of interest.
Effective and nominal rates
An effective annual rate is the actual one-year rate. A nominal annual rate is a quoted annualized rate that must be paired with a compounding frequency. For example, a nominal rate compounded monthly is divided into 12 periodic rates before compounding.
Interest rate versus discount rate
An effective discount rate measures the discount from the amount due at the end of a period back to its present value. It is related to the effective interest rate by d = i/(1+i), so the two percentages are not numerically identical.
Force of interest
The force of interest is the continuously compounded rate equivalent to an effective annual rate. It is calculated as ln(1+i). This form is common in interest theory and actuarial mathematics.
Need a complete loan schedule?
For detailed loan work, Amortization Pro creates full payment-by-payment schedules, supports extra principal and changing rates, saves loan files, exports CSV data, and prints reports. The Windows software is a $25 one-time purchase.