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 yields a higher effective annual rate?
- AInvestment B
- BCannot be determined without the principal amount.
- CBoth yield the same effective annual rate.
- DInvestment A
Show answer & explanationAnswer & explanation
Correct answer: A. Investment B
To compare, calculate the effective annual rate (EAR) for each. EAR = (1 + r/n)^(nt) - 1. For Investment A: r=0.045, n=4. EAR_A = (1 + 0.045/4)^4 - 1 ≈ 0.045765 or 4.5765%. For Investment B: r=0.044, n=12. EAR_B = (1 + 0.044/12)^12 - 1 ≈ 0.044896 or 4.4896%. Investment A has a higher EAR.
Why the other options are wrong
- B. This is incorrect; the principal amount is not needed to compare effective rates.
- C. This is incorrect; the effective rates are different.
- D. This is the correct answer; Investment A yields a higher effective annual rate.
Effective Annual Rate (EAR)
The effective annual rate (EAR) is the actual annual rate of return earned on an investment, considering the effect of compounding over a year. It allows for comparison of investments with different compounding frequencies.
- EAR = (1 + Nominal Rate / Compounding Periods)^(Compounding Periods) - 1
- Used to compare investments with different compounding frequencies
- Higher EAR means better return
Memory trick: Compound: Interest on interest, money grows like a snowball.