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2 answers:
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I'm going to assume that you are trying to find the two numbers. Based on the information in the problem, we can create the following equations (where and
are the two numbers):
We have a systems of equations. In this case, it would be easier to use elimination by adding vertically. This produces the result:
To find , substitute the value for
into one of the earlier equations:
The two numbers are 12 and 18.
Answer:
a. They will need $90,000.00 for the down payment
b. The mortgage amount (principal) will be $360,000.00
c. The monthly principal payment will be $1,500,00
The monthly interest payment will be $634.40
d. The total interest they will pay: $152,256.00
Step-by-step explanation:
house price= $450,000
down payment = 20%
20-year mortgage
Interest rate= 3.75%
a. How much they will need for the down payment?
The down payment (DoP) is 20% of the house price
DoP= 20% de $450,000
DoP= 0.20*450,000
DoP= $90,000
b. What will be the mortagage amount (the principal)?
The mortgage amount (MoA) (principal) is the difference between the house price and the down payment.
MoA= $450,000 - $90,000
MoA= $360,000
c. How much will their monthly payment be for the principal and interest?
This equation represents the monthly payment (M):
where
P= the principal = $360,000
r= monthly interest rate = 3,75% divided by 12 = 0,31%
n= number of payments = 20 years multiplied by 12 months = 240
Let´s input these data into the equation:
Solving the equation:
M= $2,134.40
the principal component of this M would be
$360,000 divided by the 240 months
So, the principal component of M = $1,500.00
And the interest component of M is the difference
$2,134.40 - $1,500.00
So, the interest component of M = $634.40
d. How much total interest will they pay if they take the full 20 years to pay off the mortgage?
With every payment, they will be paying:
$634.40 per month, multiplied by 240 months
The total interest will be $152,256.00