49. Five years ago, a borrower incurred a mortgage for S200,000 at 10 percent fo

Question

49. Five years ago, a borrower incurred a mortgage for S200,000 at 10 percent for 30 years, monthly payments. The current market rate is 8.5 percent for 25-year mortgages. The existing mortgage has a prepayment penalty of 2 percent of the payoff balance and the new lender will charge 3 percent financing cost on a new loan. The borrower's opportunity investment rate is 9 percent. If the borrower intends to hold the mortgage financing for 25 more years, should she refinance at the present time? (You must show your work)

Explanation / Answer

Step 1: Balance in existing loan:

Loan amortisation schedule:

balance in existing loan= 193148.64

Step 2: Calculation of loan amount required:

Amount required to payoff existing loan= balance * (1+prepayment penalty)= 193148.64*1.02= 197011.6

Loan amount required= Amount required to payoff existing loan/ (1-finance charge)= 197011.6/ (1-3%)= 203101.8

Step 3: monthly payment under new loan:

Step 4: calculation of present value of monthly payments:

Step 5: comparison:

since present value of future payments discounted at 9% (194882) is less than the loan amount taken ( 203105) she should refinance at present time

Period payment = [P x R x (1+R)^N]/[(1+R)^N-1] Using the formula: Principle P 200000 Rate of interest per period R 0.8333% [10%/12] Number of payments N 360 [30 years *12] Period payment using the formula 1,755.14

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