Two banks in the area offer 30-year, $180,000 mortgages at 4.7 percent and charg
ID: 2796206 • Letter: T
Question
Two banks in the area offer 30-year, $180,000 mortgages at 4.7 percent and charge a $3,700 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.)
Two banks in the area offer 30-year, $180,000 mortgages at 4.7 percent and charge a $3,700 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).
Two banks in the area offer 30-year, $180,000 mortgages at 4.7 percent and charge a $3,700 loarn 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 (Not refundable) EAR APRExplanation / Answer
Insecurity Bank and Trust (Refundable)
Step 1: Calculate Amount of Monthly Payment
The amount of monthly payment can be calculated with the use of PMT (Payment) function/formula of EXCEL/Financial Calculator. The function/formula for PMT is PMT(Rate,Nper,PV,FV) where Rate = Interest Rate, Nper = Period, PV = Present Value and FV = Future Value.
Here, Rate = 4.7%/12, Nper = 30*12 = 360, PV = 180,000 + 3,700 = $183,700 and FV = 0
Using these values in the above function/formula for PMT, we get,
Monthly Payment = PMT(4.7%/12,360,183700,0) = $952.74
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Step 2: Calculate APR
The value of APR can be arrived with the use of Rate function/formula of EXCEL/Financial Calculator. The function/formula for Rate is Rate(Nper,PMT,-PV,FV) where Nper = Period, PMT = Payment, PV = Present Value and FV = Future Value (if any).
Here, Nper = 360, PMT = $952.74, PV = $180,000 and FV = 0
Using these values in the above function/formula for Rate, we get,
APR = Rate(360,952.74,-180000,0)*12 = 4.88% [we multiply by 12 as we need to arrived at Annual Rate]
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Step 3: Calculate EAR
The value of EAR can be calculated as follows:
EAR = (1+APR/12)^12 - 1 = (1+4.88%/12)^12 - 1 = 4.99% or 5%
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I.M. Greedy and Sons Mortgage (Non Refundable)
In this case APR would be the same as quoted rate of 4.70%
The value of EAR is determined as below:
EAR = (1+APR/12)^12 - 1 = (1+4.70%/12)^12 - 1 = 4.80%
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Tabular Representation:
Insecurity Bank and Trust (Refundable) I.M. Greedy and Sons Mortgage Bank (Non Refundable) EAR 4.99% 4.80% APR 4.88% 4.70%