There are two banks in the area that offer 22-year, $730,000 mortgages at 7.60 p
ID: 2631735 • Letter: T
Question
There are two banks in the area that offer 22-year, $730,000 mortgages at 7.60 percent and charge a $4,380 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). Complete the following table: Insecurity Bank loan (refundable) APR ____%, EAR_____% Greedy and Sons loan (nonrefundable) APR ____%, EAR ____ %
Explanation / Answer
PV of loan = $730,000
730000 = R * (1-(1.076)^-22)/0.076 = R * 10.53176
R = $69,314.13
APR:
Insecurity Bank, include the fees that is refundable: net amount borrowed = 730000 - 4380 = 725620
Ratio = 69314.13/725620 = 0.095524
APR(1+APR)^22/((1+APR)^22 - 1)) = 0.095524
Solving for APR we get APR = 7.6748% = 7.67% (No easy way to solve this equation. Either look at the annuity tables or you can use excel: =RATE(22,69314.13,-725620)
I.M Greedy bank, do not include the fees as its non refundable: net amount borrowed = 730000
ratio = $69,314.13/730000 = 0.09495
APR(1+APR)^22/((1+APR)^22 - 1)) = 0.09495
Solving this will give APR = 7.6% .......Excel formula =RATE(22,69314.13,-730000)
EAR:
Assuming the compounding is monthly,
EAR = (1+APR/12)^12 - 1
Insecurity bank: EAR = (1+0.07675/12)^12 - 1 = 7.95%
IM Greedy bank: EAR = (1+0.076/12)^12 - 1 = 7.87%