Part A:
Given that Victor is buying a home for $125,340 and that he is making a 15% down payment.
The amount of down payment is given by 15% of $125,340 = 0.15 x $125,340 = $18,801.
Therefore, the amount of mortgage he needs to borrow is given by $125,340 - $18,801 = $106,539
Part B
Given that he earns a gross annual income of $64,570 and that the loan of $106,539 will be spread for 20 years at 3.75% interest.
$106,539 / 20 = $5,326.95
Roughly he will be paying about $5,000 every year which is way below his annual gross income.
Therefore, he can afford the mortgage.
Part C
The monthly mortgage payment can be calculated using the present value of annuity formula given by
[tex]PV=P\left( \frac{1-\left(1+\left( \frac{r}{t} \right)\right)^{-nt}}{ \frac{r}{t} } \right)[/tex]
where: PV is the current value of the loan, P is the periodic (monthly) payment, r is the annual interest rate, t is the number of payment in one year and n is the number of years.
Here, PV = $106,539; r = 3.75% = 0.0375; t is 12 payments in one year (since payment is to be made monthly); n = 20 years.
Thus, we have:
[tex]106,539=P\left( \frac{1-\left(1+\left( \frac{0.0375}{12} \right)\right)^{-20\times12}}{ \frac{0.0375}{12} } \right) \\ \\ =P\left( \frac{1-\left(1+0.003125\right)^{-240}}{0.003125} \right)=P\left( \frac{1-\left(1.003125\right)^{-240}}{0.003125} \right) \\ \\ =P\left( \frac{1-0.472919}{0.003125} \right)=P\left( \frac{0.527081}{0.003125} \right)=168.666P \\ \\ \Rightarrow P= \frac{106,539}{168.666} =631.66[/tex]
Therefore, the monthly mortgage payment is $631.66
Part D
Since he will make a monthly payment of $631.66 for 20 years, thus he will make a total of $631.66 x 12 x 20 = $151,598.40
Therefore, his total payment for the house will be $151,598.40
Part E
Since he will make a total payment of $151,598.40 for a mortgage loan of $106,539.
Therefore, the amount of interest he will pay is given by $151,598.40 - $106,539 = $45,059.40
