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Questions and Answers
What is the main purpose of calculating the Effective Annual Rate (EAR)?
What is the main purpose of calculating the Effective Annual Rate (EAR)?
- To simplify the calculation of monthly interest payments.
- To accurately compare interest rates quoted over different periods. (correct)
- To comply with banking regulations regarding advertised interest rates.
- To determine the Annual Percentage Rate (APR) for a loan.
If a loan has an APR of 12% and compounds monthly, which statement is most accurate?
If a loan has an APR of 12% and compounds monthly, which statement is most accurate?
- The loan's EAR is higher than 12%. (correct)
- The loan's EAR is lower than 12%.
- The loan's EAR is also 12%.
- The loan's monthly interest rate is 12%.
Which of the following accurately describes the difference between APR and EAR?
Which of the following accurately describes the difference between APR and EAR?
- APR and EAR are always equal.
- APR is used for investments, while EAR is used for loans.
- APR considers the effect of compounding; EAR does not.
- EAR considers the effect of compounding; APR does not. (correct)
What does 'm' represent in the context of interest rate calculations?
What does 'm' represent in the context of interest rate calculations?
What factor distinguishes the effective interest rate from the Annual Percentage Rate (APR)?
What factor distinguishes the effective interest rate from the Annual Percentage Rate (APR)?
A credit card advertises an APR of 18%, compounded monthly. What is the approximate effective monthly interest rate?
A credit card advertises an APR of 18%, compounded monthly. What is the approximate effective monthly interest rate?
A bank offers a savings account with an APR of 5%, compounded daily. Which statement accurately reflects the effective annual rate (EAR)?
A bank offers a savings account with an APR of 5%, compounded daily. Which statement accurately reflects the effective annual rate (EAR)?
What does 't' represent when calculating effective interest rates?
What does 't' represent when calculating effective interest rates?
Loan A has an APR of 10% compounded semi-annually. Loan B has an APR of 9.8% compounded monthly. Which loan has the lower effective annual rate (EAR)?
Loan A has an APR of 10% compounded semi-annually. Loan B has an APR of 9.8% compounded monthly. Which loan has the lower effective annual rate (EAR)?
Why is it important to understand the compounding frequency when evaluating financial products?
Why is it important to understand the compounding frequency when evaluating financial products?
Flashcards
Effective Annual Rate (EAR)
Effective Annual Rate (EAR)
The total amount of interest that is actually earned or paid on an investment, loan, or other financial product due to the effect of compounding interest.
Annual Percentage Rate (APR)
Annual Percentage Rate (APR)
The annualized interest rate without considering the effect of compounding within the year.
Compounding frequency (m)
Compounding frequency (m)
The number of times per year that interest is calculated and added to the principal of a deposit or loan.
Period (t)
Period (t)
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Study Notes
- Interest rates are quoted for various intervals like days, months, or years.
- Comparing rates quoted for different periods (e.g., monthly vs. annually) requires standardization.
Effective Annual Rate (EAR)
- EAR is a standardized interest rate to compare interest paid or received over different frequencies.
- Borrowing $100 at 1% per month results in a repayment of $112.68 after 12 months: $100 × (1.01)^12 = $112.68
- An interest rate of 1% per month is equivalent to an effective annual rate of 12.68%.
Annual Percentage Rates (APRs)
- APR is calculated by multiplying the rate per period by the number of periods in a year.
- For a loan with a 1% monthly interest rate, the APR is 12 × 1% = 12%.
Variables
- m = Compounding frequency within a year
- Indicates how many times a year interest is received on interest.
- m is provided and differs from the frequency of cash flows.
- t = The period for which the interest rate is calculated, expressed in terms of a year
- t is the length of time which equals the frequency of the cash flows.
- Timeline length is considered in present value/future value formulas.
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