Two banks in the area offer 35-year, $205,000 mortgages at 5.2 percent and charg
ID: 2614825 • Letter: T
Question
Two banks in the area offer 35-year, $205,000 mortgages at 5.2 percent and charge a $4,200 loan application fee. However, the application fee charged by Insecurity Bank and Trust is refundable if the loan application is denied, whereas that charged by I.M. Greedy and Sons Mortgage Bank is not. The current disclosure law requires that any fees that will be refunded if the applicant is rejected be included in calculating the APR, but this is not required with nonrefundable fees (presumably because refundable fees are part of the loan rather than a fee).
What are the EARs on these two loans? What are the APRs? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
I have the EAR for I.M Greedy and Sons Mortgage Bank (not refundable) as being 5.33%, which is correct because I am able to check my work and it lets me know if I am right or not. I jsut need the EAR and APR for Insecurity Bank and Trust and then the APR for I.M. Greddy and Sons Mortgage Bank.
Two banks in the area offer 35-year, $205,000 mortgages at 5.2 percent and charge a $4,200 loan application fee. However, the application fee charged by Insecurity Bank and Trust is refundable if the loan application is denied, whereas that charged by I.M. Greedy and Sons Mortgage Bank is not. The current disclosure law requires that any fees that will be refunded if the applicant is rejected be included in calculating the APR, but this is not required with nonrefundable fees (presumably because refundable fees are part of the loan rather than a fee).
Explanation / Answer
APR calculation is basically the equating the monthly mortgage payments upon the base of net loan amount (loan amount - fees) since the monthly mortgage payment will be calculated upon the gross amout of loan but what the borrower receives is net of fees.
The fees charged by Insecurity Bank & Trust are refundable hence will be included for APR calculation. Now we will first calculate the monthly mortgage payment to be made for these loans (will be same for both banks)
Monthly Payment = Loan * [r * (1+r)t] / [(1+r)t - 1] where r is the monthly interest (annual rate divided by 12) and t is time period in months. We have r = 5.2%/12 = 0.43% and t = 35*12 = 420 months
Monthly Payment = 205000 * [0.43% * (1+0.43%)420]/[(1+0.43%)420 - 1] = 1060.90
Now the net loan for Insecurity Bank & Trust = $ 205000-4200 = 200800 (since APR will be net of refundable fees).
Now to calculate APR, we basically calculate the IRR net loan (200800) and 420 monthly payments of 1060.90. Note the first payment is inflow and other 420 payments are outflows. Using excel we get the IRR rate of 0.45% per month or annual rate of 5.37% which is APR.
For EAR, we will simply use the rate 5.37% (calculated above) and since the monthly mortgage payment have inbuilt monthly compounding, we will calculate the EAR using formula = [(1+r%/m) m- 1]where m is the number of times we are compounding in a year. EAR = [(1+5.2%/12)12 - 1] = 5.50%
Similarly for I M Greedy & Sons, the APR will be same as quoted at 5.2% since we are given that the fee will not be used for calculating the APR. EAR = [(1+5.2%/12)12-1] = 5.33%