Answer:
The total amount of the mortgage is $ 871879.4
Step-by-step explanation:
Given as :
The cost of house = $ 175,000
The first 80% of mortgage amount = 80% of $ 175,000 = 140,000
The second 20 % of mortgage amount = Â 20% of $ 175,000 = 35,000
The 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 years
Let 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 × 4.02365
Or, [tex]A_1[/tex] = $ 563311
Again
[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 × 8.81624
Or, [tex]A_2[/tex] = $ 308568.4
∴ Total amount A =  [tex]A_1[/tex] +  [tex]A_2[/tex]
I.e A = $ 563311 + $ 308568.4 = $ 871879.4
Hence The total amount of the mortgage is $ 871879.4 Â answer
