MATH SOLVE

10 months ago

Q:
# You are applying for an 80/20 mortgage to buy a house costing $175,000.The first (80%) mortgage has an interest rate of 4.75%, and the second (20%)mortgage has an interest rate of 7.525%. Both the first mortgage and thesecond mortgage are 30-year fixed-rate mortgages. What will the totalamount of the mortgage be?

Accepted Solution

A:

Answer:The total amount of the mortgage is $ 871879.4Step-by-step explanation:Given as :The cost of house = $ 175,000The first 80% of mortgage amount = 80% of $ 175,000 = 140,000The second 20 % of mortgage amount = 20% of $ 175,000 = 35,000The rate of interest for 80 % mortgage = 4.75 %The rate of interest for 20 % mortgage = 7.525 %The time period for both mortgage is 30 yearsLet The amount at 80 % mortgage = [tex]A_1[/tex]And The amount at 20 % mortgage = [tex]A_2[/tex]So, From compounded method [tex]A_1[/tex] = principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]or, [tex]A_1[/tex] = 140,000 × [tex](1+\dfrac{\textrm 4.75}{100})^{\textrm 30}[/tex]Or, [tex]A_1[/tex] = 140,000 × [tex](1.0475)^{30}[/tex]Or, [tex]A_1[/tex] = 140,000 × 4.02365Or, [tex]A_1[/tex] = $ 563311Again[tex]A_2[/tex] = principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]or, [tex]A_2[/tex] = 35,000 × [tex](1+\dfrac{\textrm 7.525}{100})^{\textrm 30}[/tex]Or, [tex]A_2[/tex] = 35,000 × [tex](1.07525)^{30}[/tex]Or, [tex]A_2[/tex] = 35,000 × 8.81624Or, [tex]A_2[/tex] = $ 308568.4∴ Total amount A = [tex]A_1[/tex] + [tex]A_2[/tex] I.e A = $ 563311 + $ 308568.4 = $ 871879.4Hence The total amount of the mortgage is $ 871879.4 answer