Question 1180046
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Part (a)


Refer to this link here
https://www.mtgprofessor.com/formulas.htm
for the formula to calculate the monthly payment


The idea is to use algebra to solve for the amount loaned (L). 
In this case, 
P = 1300
c = r/12 = 0.07/12 = 0.00583333333333 approximately
n = 12*30 = 360 months


So,
{{{P = (Lc(1+c)^n)/((1+c)^n-1)}}}


{{{1300 = (L*0.00583333333333(1+0.00583333333333)^360)/((1+0.00583333333333)^360-1)}}}


{{{1300 = (L*0.04734623527284)/(7.11649747535)}}}


{{{1300*7.11649747535 = 0.04734623527284L}}}


{{{9251.446717955 = 0.04734623527284L}}}


{{{0.04734623527284L = 9251.446717955}}}


{{{L = 9251.446717955/0.04734623527284}}}


{{{L = 195399.83833228}}}


{{{L = 195399.84}}}


The largest loan you can afford is $195,399.84 when the highest monthly mortgage payment possible is $1,300.


When rounding to the nearest dollar, we must round down because rounding up will mean the monthly payment will exceed $1300. 
So we'll round $195,399.84 to $195,399


Answer: $195,399


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Part (b)


Simply multiply the monthly payment (1300) with the number of months (30*12 = 360) to get the total amount paid back to the loan company


So we get: 1300*360 = 468,000
This is both principal and interest


Answer: $468,000


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Part (c)


In the previous part, we calculated that you'll pay back a total of $468,000


Subtract off the loan amount to find the amount of interest paid back. 


total interest = (total amount paid back) - (amount loaned)
total interest = ($468,000) - ($195,399)
total interest = $272,601


Answer: $272,601
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