Question

Suppose you have two options on a $150,000, 30-year, fixed-rate mortgage. Option one is a 5.25% contract rate with 2.00 points. Option two is 5.00% contract rate but you have forgotten how many discount points are charged. Both loans have a 3% prepayment penalty for the first eight years of life. A. (1 pt) Calculate the number of points on option two that would equalize the APRs of the two loans. Answer: ________ B. (1 pt) Calculate the number of points on option two that would equalize the effective costs of the two loans over a five-year holding period. Answer: ________

Answer 1

This is solved using MS Excel. The formulas are also shown.

Option 1 Value Rate No. of years Points Value of points PMT APR 5.25% 4 30 $828.31 -PMT(5.25%/12,30*12,150000,0.) 5.43%-RATE 360,828.31,-(150000-3000),0.)*12 Option 2 Value Rate No. of years Points Value of points PMT APR Loan PV 12 5.00% 4.73-D15/D11*100 7095.57 $805.23 16 17 18 19 5.43%-D8 142904.43PV(D17/12,360,D16,,)

Option 1 Value Rate No. of years Points Value of points PMT FV after 5 years Penalty @ 3% Effective cost Option 2 Value Rate No. of years PMT FV after 5 years Penalty @ 3% Effective cost Effective loan amount Points 5.25% 30 3000 $828.31 $138,223.93 $4,146.72 6.22% -PMT(5.25%/12.30*|2,150000,0.) 10 12 5.00% $805.23 $137,743.26 $4,132.30 6.22% $143,811.40 -FV(5%/12,60,805.23,-150000.) :3%*016 16 I 18 -PV(6.22%/12,30,805.23(137743.26+4132.3).) 20 4.126 (150000-143811.4)/150000) 100 Sheet1 Ready E