Question

16 years ago, a homeowner obtained a fully amortizing loan $120,000 at eight percent interest for 30 years. Mortgage rates have dropped, so that a fully amortizing 14-year loan can be obtained today at six percent interest. There is a two-percent prepayment penalty on the mortgage balance of the original loan. In addition, the new loan will charge 3 points, and other closing costs on the new loan will add an additional $125.00. All payments and compounding are monthly.

What is the numeric value of the effective annual interest rate

Answer 1

Below is the solution, please comment if any further explanation needed!

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Explanation:

Step 1:

Existing loan:

PV = $120,000

Monthly interest rate = 8%/12

Number of months = 30 * 12 = 360 months

Monthly payment of existing loan = PMT (8%/12, 360, -120000, 0, 0) = $ 880.5175

Step 2:

Find current outstanding:

Number of remaining months = (30-16) *12 = 168 months

Current outstanding balance = PV (8%/12, 168, 880.5175, 0,0) = $88,822.9

Step 3:

Monthly payment on refinancing:

Monthly interest rate = 6%/12

Monthly payment on refinancing = PMT (6%/12, 300, -88,822.9, 0, 0) = $ 572.29

Net Monthly saving in monthly payment on refinancing = 880.5175 - 572.29 = $308.23

Step 4:

Costs on refinancing = 88,822.9 * 3% + $125.00 = $ 2,789.687

Costs of prepayment = 88,822.9 * 2% = $ 1,776.458

Total costs = $4,566.145

Step 5:

Monthly Return on investment = RATE (nper, pmt, pv, fv, 0) = RATE (168, 308.23, -4,566.145, 0, 0) = 6.75%

Annual return on investment = 6.75% * 12 = 81.00%

Return on investment if the borrower refinances = 81%