Final answer:
The rate used to compare nominal interest rates with different compounding intervals is the effective interest rate or effective annual rate (EAR), which reflects the true financial impact of compounding.
Step-by-step explanation:
The rate used to compare nominal interest rates that are equal but have different numbers of compounding intervals is known as the effective interest rate or effective annual rate (EAR). It takes into account the effect of compounding and allows for a like-for-like comparison across different compounding frequencies.
For example, if you have two bank accounts, both advertised with a nominal annual interest rate of 5%, but one compounds quarterly while the other compounds annually, the one that compounds quarterly will have a slightly higher effective annual rate due to the compounding occurring more frequently. The EAR can be calculated using the formula: EAR = (1 + (i/n))^n - 1, where 'i' is the nominal rate and 'n' is the number of compounding periods per year.
As explained in Box 1.2, the process of compounding interest is at work when money in a bank account grows at a certain interest rate over time. Even a small change in interest rates can result in a significant difference in the future value of an investment due to compound interest.