Please show work using the BAII Calculator steps please. 2. Suppose that you are
ID: 2782492 • Letter: P
Question
Please show work using the BAII Calculator steps please. 2. Suppose that you are considering a loan in which you will borrow $275,000 using a 30-year loan. The loan has an annual interest rate of 15% with monthly payments and monthly compounding. Suppose also that the lender is charging you a 0.75% origination fee, you are paying 3 points in order to get the 15% interest rate, and the loan has $675 in third-party closing costs associated with it. a. What will the effective borrowing cost be for this loan if you make all of the scheduled payment? b. What will the lender’s yield be for this loan if you make all of the scheduled payments? c. What will the effective borrowing cost be for this loan if you pay off the loan at the end of the 4th year?
Explanation / Answer
Mortgage Amount =$275,000
Time =30 years
Rate of Interest =15% or 1.25% monthly
Monthly Payment under this plan=PMT(0.0125, 360, 275000) =$3,477.22
Origination Fee =0.75%
Points Paid = 3points
Third Party closing costs=$675
a.) Let y be the effective monthly borrowing cost,
275,000 = (0.03 + 0.0075)x275,000 + 675 + 3477.22x{(1-(1+y)-360)/y}
275,000 = 10,312.50 + 675 + 3,477.22x{(1-(1+y)-360)/y}
264,012.50 = 3,477.22x{(1-(1+y)-360)/y}
75.9263 = {(1-(1+y)-360)/y}
Using Trial and Error method to solve for y,
y = 0.013047
Hence, annual effective rate =12x0.013047 = 15.6562%
b.) For evaluating lenders yield, we need to consider only the payments which were made to lender, i.e.
275,000 = (0.03 + 0.0075)x275,000 + 3477.22x{(1-(1+y)-360)/y}
275,000 = 10,312.50 + 3,477.22x{(1-(1+y)-360)/y}
264,687.50 = 3,477.22x{(1-(1+y)-360)/y}
76.1204 = {(1-(1+y)-360)/y}
Using Trial and Error method to solve for y,
y = 0.013012
Hence, annual yield for lender =12x0.013012 = 15.6143%
c.) Loan outstanding at the end of 4th year =$272,409
Let y be the effective monthly borrowing cost,
275,000 = (0.03 + 0.0075)x275,000 + 675 + 3477.22x{(1-(1+y)-48)/y} + 272,409/(1+y)48
275,000 = 10,312.50 + 675 + 3,477.22x{(1-(1+y)-48)/y} + 272,409/(1+y)48
264,012.50 = 3,477.22x{(1-(1+y)-48)/y} + 272,409/(1+y)48
75.9263 = {(1-(1+y)-48)/y} + 78.3410/(1+y)48
Using Trial and Error method to solve for y,
y = 0.021155
Hence, annual effective rate =12x0.021155 = 25.3857%