Answer:
[tex][/tex]
a) $183,915.26
b) $504,001.84
c) $320,086.58
Step-by-step explanation:
[tex][/tex] a) To find the maximum affordable loan amount, we can use the formula for the monthly payment on a mortgage:
[ P = \dfrac{r \cdot V}{1 - (1 + r)^{-n}} ]
where ( P ) is the monthly payment, ( r ) is the monthly interest rate, ( V ) is the loan amount, and ( n ) is the total number of payments. Solving for ( V ), we find ( V = \dfrac{P(1 - (1 + r)^{-n})}{r} = dfrac{1400(1 - (1 + 0.077/12)^{-30*12})}{0.077/12} = 183915.26 ).
b) The total money paid to the loan company can be found using the formula:
[ text{Total Payment} = P \times n ]
where ( P ) is the monthly payment and ( n ) is the total number of payments. So, the total payment is ( 1400 \times 12 \times 30 = 504001.84).
c) The total interest paid can be found by subtracting the initial loan amount from the total payment:
[ text{Total Interest} = text{Total Payment} - \text{Loan Amount} = 504001.84 - 183915.26 = 320086.58 ).
Extra information: The calculations assume that the interest is compounded monthly.
