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Multiple Choice
A loan has an APR of 8.5\% and an EAR of 8.5\%. Given this, the loan must:
A
Compound interest quarterly.
B
Compound interest semiannually.
C
Charge interest only once per year.
D
Have monthly compounding.
Verified step by step guidance
1
Understand the difference between APR (Annual Percentage Rate) and EAR (Effective Annual Rate). APR is the nominal interest rate, while EAR accounts for compounding within the year.
Recognize that when APR equals EAR, it implies there is no compounding within the year. This is because compounding would cause the EAR to be higher than the APR.
Analyze the compounding options provided in the problem: quarterly, semiannually, monthly, or annually. Compounding quarterly, semiannually, or monthly would result in an EAR greater than the APR.
Conclude that the only scenario where APR equals EAR is when interest is charged only once per year, meaning there is no intra-year compounding.
Verify the logic by recalling the formula for EAR: EAR = (1 + (APR/n))^n - 1, where 'n' is the number of compounding periods per year. If n = 1 (annual compounding), EAR = APR.