A $100,000 loan can be obtained at a 10 percent rate with monthly payments over a 15-year term.

a. What is the after-tax effective interest rate on the loan, assuming the borrower is in a 30 percent tax bracket and the loan is held only three years? Assume that the benefit of interest deductions for tax purposes occurs at the same time payments are made

b. Calculate the after-tax effective cost for the above loan, assuming 5 points are charged and that the points are tax-deductible at the time they are paid

Please show steps in finding the solution similar to the file attached. It makes it easy for me to figure out how you got to your solution.

Solution Loan Amount Interest Rate Time (in years) n Desired Mortgage Loan Yield If 9% rate is charged, then PMT becomes: PMT (a) $ 95,000.00 9% 25 300 10% $ (Assuming monthly payments) -797.24 If the lender wants to charge the origination fee, such that PMT remains $8550 while yield on loan comes out to be 10%, then: PMT $ 797.24 Interest 10% n 300 Present Value/ Disbursement to be made $ -87,734.05 Origination Fee $ 7,265.95 7.6% Therefore, the mortgage lender should disburse $87,734 and cut an origination fee of $7,265(or 7.6%) to make 10% yield on the loan. (b) If loan is expected to be repaid in 10 years Monthly Payments with 9% interest rate $ 797.24 If, Interest Rate n PMT Outstanding Loan Balance at the end of 10 years 9% 180 $ 797.24 $ -78,602.61 Therefore, if we expect repayment after 10 years, then Future Value Desired Interest Rate n PMT Present Value/ Disbursement to be made $ 78,602.61 10% 120 $ 797.24 $ -89,364.43 Origination Fee $ 5,635.57 5.93% Therefore, if repayment is expected after 10 years, then mortgage lender should charge %5635.57 or 5.93% origination fee in order to achieve 10% yield on on mortgage loan