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
|I. M. Greedy and Sons Mortgage Bank (Nonrefundable)|
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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