<h3>
Answer: $975.63 per month</h3>
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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
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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.
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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
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The last step is to add the two monthly payments (found at the conclusion of each previous section)
730.31 + 245.32 = 975.63
