Question 1181795: You can afford a $1200 per month mortgage payment. You've found a 30 year loan at 7% Interest. A. How big of a loan can you afford? B) How much total money will you pay the loan company? C) How much of that money is Interest?
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Part A
We'll use this formula
P = (L*i)/( 1-(1+i)^(-n) )
where
P = monthly payment
L = loan amount
i = r/12, r is the interest rate
n = number of months
In this case,
P = 1200
L = unknown
i = r/12 = 0.07/12 = 0.00583333333333 (approx)
n = 12y = 12*30 = 360 months
We'll plug those known values in to find the unknown value L
P = (L*i)/( 1-(1+i)^(-n) )
1200 = (L*0.00583333333333)/( 1-(1+0.00583333333333)^(-360) )
1200 = (0.00583333333333L)/0.87679414636214
1200*0.87679414636214 = 0.00583333333333L
1052.15297563457 = 0.00583333333333L
0.00583333333333L = 1052.15297563457
L = 1052.15297563457/0.00583333333333
L = 180369.081537458
L = 180369.08
Answer: $180,369.08
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Part B
If you pay $1200 per month for 360 months (aka 30 years), then you'll pay back a total of 1200*360 = 432,000 dollars.
This includes principal (the result of part A) and interest on top of it.
Answer: $432,000
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Part C
Subtract the results of B and A to get
B-A = (total paid back) - (principal)
B-A = (432,000) - (180,369.08)
B-A = 251,630.92
Answer: $251,630.92
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