Question

(Please show step by step workings)

Maria and John have been married for 2 years and are trying to start a family.

They have been renting a small apartment and decide they want to purchase a house.

They find one that is selling for $450,000. They have been advised to make a 20% down payment.

1. If they make a 20% down payment on a 20-year mortgage at 3.75%,

a. How much will they need for the down payment?

b. What will be the mortgage amount (ie the principal)

c. How much will their monthly payment be for the principal and interest?

d. How much total interest will they pay if they take the full 20 years to pay off the mortgage?

Answer 1

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

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):

`M=P (r(1+r)^(n) )/((1+r)^(n)-1)`

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:

`M= 360,000(0.0031(1+0.0031)^(240) )/((1+0.0031)^(240) -1)`

`M= 360,000(0.0031(1.0031)^(240) )/((1.0031)^(240) -1)`

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