Question

# There are two banks in the area that offer 25-year, \$330,000 mortgages at 4.8 percent compounded...

There are two banks in the area that offer 25-year, \$330,000 mortgages at 4.8 percent compounded monthly and charge a \$4,800 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.)

 Insecurity Bank and Trust (Refundable) I. M. Greedy and Sons Mortgage Bank (Nonrefundable) EAR % % APR % %

Insecurity Bank and Trust:

In order to get a loan of 330,000, the total amount required is 330,000 + refundable fee = 330,000+4,800 = 334,800

Monthly payment for this loan amount is: PV = 334,800; N = 25*12 = 300; rate = 4.8%/12 = 0.4%, solve for PMT.

PMT = 1,918.39

Now, using this monthly payment, calculate the rate for the loan of 330,000: PMT = -1,918.39; PV = 330,000; N = 300, solve for RATE.

Monthly rate (r) = 0.4120%

EAR = [(1+ r)^12] -1 = ((1+0.4120%)^12)-1 = 5.06%

APR = r*12 = 0.4120%*12 = 4.94%

I. M. Greedy and Sons Mortgage Bank:

Since the fee is non-refundable, the APR for this loan is the quoted APR of 4.80% only.

EAR = [(1+APR/12)^12] -1 = [(1+4.80%/12)^12] -1 = 4.91%

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