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Sagot :
Answer:
(a) The mortgage amount she will borrow is $180,400
(b) Yes she can
(c) Her monthly payment will be approximately $914.06
(d) Her total repayment is approximately $329,061.6
(e) The amount of interest is approximately $148,661.6
Step-by-step explanation:
The details of the transactions are;
The gross annual income Victoria earns = $124,482
The cost price of the home she is buying, C = $225,500
The amount she is making as down payment = 20%
The duration the loan she id financing the rest with, t = 30-years
The interest rate on the loan, r = 4.5%
(a) The mortgage amount she will borrow, 'P', is the cost of the home less the down payment
The down payment = 20% of the cost of the home
∴ The down payment = (20/100) × $225,500 = $45,100
∴ P = $225,500 - $45,100 = $180,400
The mortgage amount she will borrow, P = $180,400
(b) Using the 2× to 2.5× gross income rule, we have;
2 × her annual income = 2 × 124,482 = 248,964
∴ 2 × her annual income > The mortgage = 180,400
She can afford the mortgage
(c) The monthly fixed payment for the mortgage is given as follows;
[tex]M = P \times \dfrac{r}{n} \times \dfrac{\left(1+ \dfrac{r}{n} \right)^{n \cdot t}}{\left[\left(1 + \dfrac{r}{n} \right)^{n\cdot t} - 1\right]}[/tex]
Where;
n = The number of periods per year = 12 monthly periods per year
180,400*0.045*(1 + 0.045)^(30)/((1 + 0.045)^(30) - 1)
[tex]M = 180,400 \times \dfrac{0.045 }{12} \times \dfrac{\left(1+\dfrac{0.045 }{12}\right)^{30 \times 12}}{\left[\left(1 + \dfrac{0.045 }{12}\right)^{30 \times 12} - 1\right]} \approx 914.060298926[/tex]
Her monthly payment will be M ≈ $914.06
(d) The total repayment is given as follows;
n × t × M
∴ 12 × 30 × 914.06 = 329061.6
The total payment for the house = $329,061.6
(e) The amount of interest = The total payment - The principal loan amount
∴ The amount of interest = $329061.6 - $180,400 = $148,661.6
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