Leonard is evaluating a $400,000 mortgage. He can get a 30-year 6 percent fixed-rate mortgage with principal and interest payments of $2,398.20 with no points. He can also get a 5.75 percent mortgage loan (payments of $2,334.29) with two points. Using simple arithmetic, how many months will it take him to break even on the lower interest rate loan?

Points are an upfront charge by the lender that is part of the price of a mortgage. Points are expressed as a percent of the loan amount, with 2 points being 2%. On a $400,000 loan,

solutions  

Loan Amount                 $400,000  

Loan Term (in months)        360 months

                     mortgage I   mortgage II

Interest Rate                    6.000%5.750%  

            Points                      0.00%2.00%  

Loan Payment Amount$2,398.20$2,334.29        

Costs Over 30 — Year Period

Points Paid in Cash                      $0               $8,000

Monthly Costs -

Principal and Interest             $863,348             $840,340

Lost Interest

On Points                                      $0                        $0

On Monthly Costs                         $0                        $0

Total Costs                                 $863,348              $848,340

Reduction in Loan Balance    $400,000               $400,000

Total Cost Offsets                   $400,000               $400,000

Cost Net of Offsets                  $463,348               $448,340

Conclusions - Based on a 30 Year Holding Period    

Over the next 30 years the High Interest / Low Points Loan Will Save You:  $15,008

In Months, the Break-even Point Occurs in  1 months

In Years, the Break-even Point Occurs in        0.0833 years

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