GMAT Focus EditionQuantitative ReasoningMedium
A financial manager is comparing two investment options. Option 1 offers a 7% annual interest rate compounded annually. Option 2 offers a 6.8% annual interest rate compounded semi-annually. Which option provides a higher effective annual interest rate?
- AOption 1
- BOption 2
- CBoth options provide the same effective annual interest rate.
- DThe effective annual interest rate cannot be determined without the principal amount.
Show answer & explanationAnswer & explanation
Correct answer: B. Option 2
To compare investment options with different compounding frequencies, the effective annual interest rate (EAR) must be calculated for each. The option with the higher EAR is the better choice for returns. Option 2, despite a lower nominal rate, has a higher EAR due to more frequent compounding.
Why the other options are wrong
- A. Option 1's EAR is 7%, which is lower than Option 2's EAR.
- C. The EARs are not the same due to different compounding frequencies.
- D. The principal amount is not needed to calculate the effective annual interest rate.
Effective Annual Interest Rate (EAR)
The effective annual interest rate (EAR) is the actual annual rate of return earned or paid on an investment or loan, taking into account the effect of compounding interest.
- EAR accounts for compounding frequency.
- It allows comparison of investments with different compounding periods.
- EAR is always greater than or equal to the nominal rate if compounding occurs more than once a year.
Memory trick: Effective Rates Make All Investments Clearer.