Question

3. Suppose that you are considering a loan in which you will borrow $245,000 using a 30-year loan. The loan has an annual interest rate of 6% with monthly payments and monthly compounding. Suppose also that the lender is charging you a 0.75% origination fee, you are paying 2.25 points in order to get the 6% interest rate, and the loan has $1,275 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 7th year?

PLEASE USE A CALCULATOR (BA II PLUS) IF POSSIBLE. (Unless the Excel is outlined specifically and accurately).

Answer 1

Answer :

Calcualting the loan emi based on $245,000 borrowing

P : Monthly emi

r : monthly interest rate = 6%/12 = 0.5%

t : time in months = 30*12 = 360 months

A ; amount = 245,000

A = (P/r)*(1/(1+r)^t)

245000 = (P/0.5%)/(1-1/(1+0.5%)^360)

P = $1468.9

Calculating the effective borrowing cost

Let r be the effcetive monthly borrowing cost

Origination fee = 0.75% * 245000 = 1837.5

Points fee = 2.25% *245000 = 5512.5

Third party closing cost = 1275

Effective borrowing = 245000 - 1837.5 - 5512.5 - 1275 = 236375

236375 = (1468.9/r)/(1-1/(1+r)^360)

Solving this equation we get r = 0.53% per month

(a). Effective borrowing cost = 0.53%*12 = 6.34% per annum compounded monthly

(b). Lender yield?

P = $1468.9

Let y be the effective monthly borrowing cost

Origination fee = 0.75% * 245000 = 1837.5

Points fee = 2.25$*245000 = 5512.5

Effective borrowing = 245000 - 1837.5 - 5512.5 = 237650

237650 = (1468.9/y)/(1-1/(1+y)^360)

Sovling this equation we get y = 0.523% per mo nth

Lender Yield = 0.523%*12 = 6.29% per annum compounded monthly

(c). Lender yield will remain the same is 6.29% per annum compounded monthly despite early payment.