1) Leslie and Ben are interested in a $250,000 fully amortizing loan and are deciding between 2 options, mortgage A and mortgage B

Mortgage A

Loan term: 30 years

Annual interest rate: 5.75 %

Monthly payments

Up-front financing costs: $4,500

Discount points: 2.5

Mortgage B

Loan term: 15-years

Annual interest rate: 5.25 %

Monthly payments

Up-front financing costs: $7,500

Discount points: 2.5

a.)  Calculate the monthly payments for mortgage A and B.

b.)  Calculate the effective borrowing cost for or mortgage A and B.

c.)  Calculate Lender's Yield for or mortgage A and B

d.)  Suppose you are the borrower. Based on the effective borrowing costs, which loan would you choose? Explain your answer in

e.)  Suppose you are the lender. Based on the lenders yield, which loan would you prefer? Explain your answer in

a.)  Monthly Payments 

Mortgage A: $1361.22

Mortgage B: $1,928.49    

                 

b.)  Effective Borrowing Cost 

Mortgage A: 3.43%

Mortgage B: 3.03%

 

c.)  Lender's Yield 

Mortgage A: 3.52%

Mortgage B: 3.20%

 

d.) Mortgage B

 

e.) Mortgage A

Step-by-step explanation

Assumptions:

• 1 Discount Point = 1% of Loan Amount

 

Therefore Cost of 2.5 Discount Points = 2.5*(1%*$250,000)

= $ 6,250

 

• 1 Discount Point reduces the interest rate by one-quarter of a percent 

Therefore Interest Rates (reduced by 2.5 discount points) for Mortgage A 

= 5.75 %-(0.25%*2.5) 

= 5.125%

Monthly Interest Rates for Mortgage A

= 5.125%/12

= 0.42708333%

 Interest Rates (reduced by 2.5 discount points) for Mortgage B

= 5.25 %-(0.25%*2.5) 

= 4.625%

Monthly Interest Rates for Mortgage B

= 4.625%/12

= 0.38541667%

a.) Calculation of Monthly Payments:

Using the formula for Monthly Payments

Monthly Payments = [Loan Amount * Monthly Interest Rate * ((1+ Monthly Interest Rate)^Loan Term in Months)] / [((1+ Monthly Interest Rate)^Loan Term in Months) - 1]

Mortgage A: Monthly Payments =

[$250,000 * 0.42708333% * ((1+ 0.42708333%)^360)] / [((1+ 0.42708333%)^360) - 1]

Monthly Payments = $1361.22

Mortgage B: Monthly Payments =

[$250,000 * 0.38541667% * ((1+ 0.38541667%)^180)] / [((1+ 0.38541667%)^180) - 1]

Monthly Payments = $1,928.49

b.) Calculation of Effective Borrowing Cost :

Effective Borrowing Cost = [[((Loan related Fees + Interest Payment )/ Net Loan Amount)/number of days in loan term]*365]*100

Mortgage A: 

Net Loan Amount = Loan Amount - Discount Points Cost

= $250,000- $6,250

= $243,750

Loan related Fees = $4,500

Interest on Loan = (Monthly Payments *12*30)- Net Loan Amount

= ($1361.22*12*30)-$243,750

=$246,288.27

Effective Borrowing Cost = [[(($4,500 + $246,288.27 )/ $243,750)/(365*30)]*365]*100

      = 3.43%

Mortgage B: 

Net Loan Amount = Loan Amount - Discount Points Cost

= $250,000- $6,250

= $243,750

Loan related Fees = $7,500

Interest on Loan = (Monthly Payments *12*15)- Net Loan Amount

= ($1,928.49*12*15)-$243,750

= $103,378.73

Effective Borrowing Cost = [[(($7,500 + $103,378.73 )/ $243,750)/(365*15)]*365]*100

= 3.03%

c.) Calculation of Lender's Yield:

Lender's Yield = [[((Loan related Receipt +Discount points Costs +Interest Payment )/ Net Loan Disbursed)/number of days in loan term]*365]*100

Mortgage A: 

Net Loan Disbursed = Loan Amount - Discount Points Cost

= $250,000- $6,250

= $243,750

Loan related Receipt = $4,500

Interest on Loan = (Monthly Payments *12*30)- Net Loan Amount

= ($1361.22*12*30)-$243,750

=$246,288.27

Effective Borrowing Cost = [[(($4,500+$6,250+$246,288.27 )/ $243,750)/(365*30)]*365]*100

= 3.52%

Mortgage B: 

Net Loan Disbursed = Loan Amount - Discount Points Cost

= $250,000- $6,250

= $243,750

Loan related Receipt = $7,500

Interest on Loan = (Monthly Payments *12*15)- Net Loan Amount

= ($1,928.49*12*15)-$243,750

= $103,378.73

Effective Borrowing Cost = [[(($7,500 +$6,250+$103,378.73 )/ $243,750)/(365*15)]*365]*100

= 3.20%

d.) With the perspective of a borrower, the Mortgage costing at lower annual percentage rate is preferable as Mortgage A has a Borrowing APR of 3.43% which is higher than the Borrowing APR of Mortgage B i.e. 3.03%, Mortgage B should be selected.

e.) With the perspective of the lender, the return on Mortgage at higher annual percentage rate is preferable as Mortgage A has an APR of 3.52% which is higher than the APR of  Mortgage B i.e. 3.20% Therefore, Mortgage A should be selected.