Praxis Core Academic Skills for Educators: Mathematics (5733)Number and QuantityHard
A financial analyst is comparing two investment options. Investment A offers an annual interest rate of 4.5% compounded quarterly. Investment B offers an annual interest rate of 4.4% compounded monthly. Which investment has a higher effective annual rate (EAR)?
- AInvestment B
- BInvestment A
- CCannot be determined without the principal amount
- DBoth have the same EAR
Show answer & explanationAnswer & explanation
Correct answer: B. Investment A
To compare, calculate the EAR for each investment using the formula EAR = (1 + r/n)^n - 1, where r is the annual rate and n is the number of compounding periods per year. The principal amount is not needed for this comparison.
Why the other options are wrong
- A. Investment B has a slightly lower EAR despite more frequent compounding, due to its lower nominal rate.
- C. The EAR is independent of the principal amount; it only depends on the nominal rate and compounding frequency.
- D. The rates and compounding frequencies are different, leading to different EARs.
Effective Annual Rate (EAR)
The effective annual rate (EAR) is the actual annual rate of interest paid on an investment or loan, taking into account the effect of compounding over the year.
- It allows for comparison of investments with different compounding frequencies.
- Formula: EAR = (1 + r/n)^n - 1, where r is nominal annual rate, n is compounding periods per year.
- Always equal to or greater than the nominal annual rate for n > 1.
Memory trick: Compare with EAR, Not Just Nominal!