Find the APR, or stated rate, in each of the following cases
EAR:
12.4 semianually
13.3 monthly
11.0 weekly
14.7 infintely
Find the ear of 9.50% quarterly
To find the APR (Annual Percentage Rate) or stated rate for each of these cases, we need to convert the given Effective Annual Rates (EAR) to APR.
1. EAR of 12.4% semiannually:
To convert it to APR, we need to determine the number of compounding periods per year. Since it is semiannual compounding (twice a year), the compounding periods per year is 2.
To calculate the APR, we can use the formula:
APR = (1 + r/c)^c - 1
where r is the EAR and c is the number of compounding periods per year.
For this case, the calculation would be:
APR = (1 + 0.124/2)^2 - 1 = 0.125596 - 1 = 0.251192 or 25.1% (rounded to one decimal place).
2. EAR of 13.3% monthly:
To convert it to APR, we need to determine the number of compounding periods per year. Since it is monthly compounding (12 times a year), the compounding periods per year is 12.
Using the same formula mentioned earlier, the calculation would be:
APR = (1 + 0.133/12)^12 - 1 = 0.139622 - 1 = 0.139622 or 13.9% (rounded to one decimal place).
3. EAR of 11.0% weekly:
To convert it to APR, we need to determine the number of compounding periods per year. Since it is weekly compounding (52 times a year), the compounding periods per year is 52.
Applying the formula, we get:
APR = (1 + 0.11/52)^52 - 1 = 0.11255 - 1 = 0.11255 or 11.3% (rounded to one decimal place).
4. EAR of 14.7% infinitely:
To convert an infinitely compounded EAR to APR, we can directly use the EAR as the APR value. Therefore, in this case, the APR is 14.7%.
Remember that the APR represents the interest rate on an annual basis, so it allows for easy comparison between different loans or financial products.