Question

A bank offers 30-year, $195,000 mortgages at 5.0 percent and charges a $4,000 refundable loan application fee. The current disclosure law requires that any fees that will be refunded if the applicant is rejected be included in calculating the APR.

What is the APR that they are required to disclose? (Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16))

Insecurity Bank and Trust (Refundable) _____% 

APR _____%

Answer 1

Monthly Payment

Loan amount = $195,000

Charges = $4,000

 

Total loan amount, PV = Loan amount + Charges

PV = 195,000 + 4,000

PV = $199,000

 

Mortgage rate = 5%

M = Number of months in a year = 12

Monthly rate, RATE = Mortgage rate/M

RATE = 5%/12

RATE = 0.4166666667%

 

Monthly payment (PMT) is calculated using excel's PMT function.

Loan term = 30 years

 

Number of monthly payments, NPER = Loan term * M

NPER = 30 * 12

NPER = 360

 

Monthly payment, PMT = $1,068.28

 

Since the loan application fee is refundable, now we consider only the loan amount to calculate APR.

Loan amount, PV = $195,000

NPER = 360

PMT = $1,068.28

 

(As calculated above).

We use excel's RATE function to calculate the monthly rate and then multiply by 12 to get APR.

RATE = 0.43161246%

APR = RATE * M

APR = 0.43161246% * 12

APR = 5.18%

 

Formulae: