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Harry took out an 80/20 mortgage to buy a house costing $175,000. The first

(80%) mortgage has an interest rate of 4.75%, and the second (20%)
mortgage has an interest rate of 7.525%. Both the first mortgage and the
second mortgage are 30-year fixed-rate mortgages. What is his total
mortgage payment for this house?

2 Answers

12 votes

Answer:

WEll the answer is d

Step-by-step explanation:

The first (80%) mortgage has an interest rate of 4.75%, and the second (20%) mortgage has an interest rate of 7.525%. Both are 30-year fixed-rate mortgages.

User Adam Houldsworth
by
4.2k points
7 votes

Answer: $975.63 per month

======================================================

Step-by-step explanation:

The formula we'll be using is

P = (L*i)/( 1-(1+i)^(-n) )

where,

  • P = monthly payment
  • L = loan amount
  • i = interest rate per month in decimal form
  • n = number of months

---------------------

For the first mortgage (80%), we need to find out the L value

L = 80% of 175,000 = 0.80*175,000 = 140,000

The monthly interest rate is the annual rate over 12

i = r/12 = 0.0475/12 which I'll keep as a fraction

Lastly, this mortgage goes for 30 years aka 30*12 = 360 months. So n = 360.

To summarize the input values we'll use, we have,

  • L = 140,000
  • i = 0.0475/12
  • n = 360

Let's compute the monthly payment

P = (L*i)/( 1-(1+i)^(-n) )

P = (140,000*0.0475/12)/( 1-(1+0.0475/12)^(-360) )

P = 730.30627110436 approximately

P = 730.31

The first mortgage has a monthly payment of $730.31

We'll use this later.

---------------------

Now onto the second mortgage (20%)

L = 20% of 175,000 = 0.20*175,000 = 35,000

i = r/12 = 0.07525/12 which I'll keep in fraction form

n = 360 months (same as before)

In short,

  • L = 35,000
  • i = 0.07525/12
  • n = 360

So,

P = (L*i)/( 1-(1+i)^(-n) )

P = (35,000*0.07525/12)/( 1-(1+0.07525/12)^(-360) )

P = 245.32451498724 approximately

P = 245.32

The second mortgage has a monthly payment of $245.32

---------------------

The last step is to add the two monthly payments (found at the conclusion of each previous section)

730.31 + 245.32 = 975.63

User Gisellet
by
5.2k points