Question6 Which statement is true regarding the preferences of borrowers and savers in relation to EAR?Select one alternative: Borrowers prefer lower EAR, while savers prefer higher EAR. EAR is irrelevant to both borrowers and savers. Borrowers prefer higher EAR, while savers prefer lower EAR. Both borrowers and savers prefer higher EAR. ResetMaximum marks: 1 Flag question undefined

Question

BlackTom AI · Accepted Answer

Effective Annual Rate (EAR) measures the true annual interest rate after accounting for compounding: EAR = (1 + r/m)^m − 1, where r is the nominal rate and m is compounding periods. EAR determines what borrowers actually pay and savers actually earn over a year.

1. Relevant knowledge points and concepts
- EAR is the actual yearly cost or return including compounding.  
- For borrowers, EAR equals the effective cost of borrowing (higher EAR → higher dollars paid).  
- For savers/investors, EAR equals the effective return (higher EAR → greater dollars received).

2. Step-by-step reasoning
- Compare two EARs on the same principal: a borrower will prefer the scenario that minimizes the total interest paid; a saver will prefer the scenario that maximizes interest earned. Thus borrowers want lower EAR, savers want higher EAR.

3. Example calculations (intermediate steps)
- Take principal = $1,000 for one year. If EAR = 10%: interest = $1,000 × 0.10 = $100. If EAR = 5%: interest = $1,000 × 0.05 = $50. For a borrower, $50 paid is better than $100. For a saver, $100 earned is better than $50.

4. Why the correct answer is correct
- The EAR directly determines money flows: borrowers minimize interest payments by choosing loans with lower EAR; savers maximize interest income by choosing investments with higher EAR. This makes the statement "Borrowers prefer lower EAR, while savers prefer higher EAR." correct.

5. Why other options are incorrect
- "EAR is irrelevant to both" is false because EAR changes actual cash flows.  
- "Borrowers prefer higher EAR, while savers prefer lower EAR" reverses incentives and is incorrect.  
- "Both borrowers and savers prefer higher EAR" is wrong because higher EAR benefits savers but penalizes borrowers.

6. Conclusion
The correct choice is: "Borrowers prefer lower EAR, while savers prefer higher EAR." This matches the provided answer.

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