Final answer:
The APR and EAR on the loan are 6.00% and 6.17%, respectively. The APR is found by considering the nominal interest rate and any additional fees or costs associated with the loan. The EAR takes into account the effects of compounding and is calculated using the nominal interest rate and the number of times interest is compounded per year.
Step-by-step explanation:
The APR and EAR on the loan are 6.17% and 6.00%, respectively.
To find the APR (Annual Percentage Rate), we need to consider the nominal interest rate and any additional fees or costs associated with the loan. In this case, the mortgage rate quoted is 0.5% per month. To find the APR, we multiply this rate by 12 (months in a year) to get 6% (0.5% x 12 = 6%).
The EAR (Effective Annual Rate) takes into account the effects of compounding. Since the quoted mortgage rate is monthly, we need to calculate the EAR to determine the true annual interest rate. Using the formula for EAR, which is (1 + r/n)^n - 1, where r is the nominal interest rate and n is the number of times interest is compounded per year, we can calculate the EAR. In this case, since the mortgage rate is monthly, n is 12 and the nominal interest rate is 0.5%. Plugging in these values, we get (1 + 0.005/12)^12 - 1 ≈ 6.17%.
Therefore, the APR is 6.00% and the EAR is 6.17%.