Question

You plan to buy a $240000 home with a 10% down payment. The bank you want to finance the purchase suggests two options (use semiannual compounding): Option 1: 20-year mortgage at 8.12% APR Option 2: 30-year mortgage at 10.45% APR. What is the equivalent monthly interest rate for each option? Equivalent monthly interest rate Option 1: Equivalent monthly interest rate Option 2: What is the monthly payment of each option? Monthly payment Option 1: $ Monthly payment Option 2: $

Answer 1

Calculate the equal monthly interest rate for each option: Option 1 8.12% Option 2 10.45% 2 Particulars Annual interest rate Number of Semi annual payments per year Effective monthly interest rate Number of months in a year Equivalent monthly interest rate 8.2848% 12 10.7230% 12 0.8936% 0.6904% Hence, the Equal monthly interest rate for option 1 is 0.6904% and for option 2 is 0.8936%. Calculations: Option 2 0.1045 А 1 Particulars Option 1 2 Annual interest rate 0.0812 3 Number of Semi annual payments per year 2 4 Effective monthly interest rate =((1+B2/2) 2)-1 5 Number of months in a year 6 Equivalent monthly interest rate =+B4/B5 2 =((1+C2/2)^2)-1 12 12 =+C4/C5

Calculate the monthly payment for each option: Particulars Monthly interest rate, Rate Number of monthly installments, NPER Initial loan amount, PV Balance in loan at the end, FV Monthly installement type, TYPE Equal monthly payment required Option 1 Option 2 0.6904% 0.8936% 240 360 2160001 216000 ol 0 $1,845.18 $2,011.97 Hence, the monthly payment for option 1 is $1845 and for option 2 is $2012. Calculations: А с 10 Particulars 11 Monthly interest rate, Rate 12 Number of monthly installments, NPER 13 Initial loan amount, PV 14 Balance in loan at the end, FV 15 Monthly installement type, TYPE 16 Equal monthly payment required Option 1 0.006904 240 =240000*(1-10%) Option 2 0.008936 360 =240000*(1-10%) =PMT(B11.B12,-B13.B 14.B15) I=PMT(C11,C12,-C13.014,C15)