Question 1203888: you can afford $1,500 per month mortgage payment. you've found a 30 years loan at 6% 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
Found 2 solutions by Theo, math_tutor2020:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the calculator at https://arachnoid.com/finance/ can help you find the answer to this problem.
inputs are:
present value = 0
future value = 0
number of time periods is 30 years * 12 = 360 months
interest rate per time period is 6% per year / 12 = .5% per month.
payments are made at the end of each time period.
here are the results.
a) how big of a loan can you afford?
calculator says that present value = 250,187.42.
that's the amount of money you can get a mortgage for.
b)how much total money will you pay the loan company?
360 months * 1500 per month = total amount paid of 540,000.
c) how much of that money is interest?
540,000 minus 250,187.42 = total interest paid of 289,812.58.
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
Answers:
(a) $250,187.42
(b) $540,000
(c) $289,812.58
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Explanation for part (a)
Monthly payment formula
P = (L*i)/( 1-(1+i)^(-n) )
where,
P = monthly payment
L = loan amount
i = monthly interest rate in decimal form
n = number of months
For this problem:
P = 1500
L = unknown
i = 0.06/12 = 0.005 exactly
n = 30*12 = 360 months
Let's solve for L
P = (L*i)/( 1-(1+i)^(-n) )
1500 = (L*0.005)/( 1-(1+0.005)^(-360) )
1500 = 0.00599550525152L
L = 1500/0.00599550525152
L = 250,187.421588817
L = 250,187.42
The largest loan you can afford is $250,187.42
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Explanation for part (b)
Over the course of 360 months (aka 30 years), you pay $1500 a month.
This assumes you go with the max you can afford.
360*($1500) = $540,000 is the amount paid back.
This consists of the principal (aka loan amount) of $250,187.42 calculated back in part (a), and also consists of interest as well.
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Explanation for part (c)
Subtract the results of parts (a) and (b) to compute the total interest.
interest = (total amount paid back) - (loan amount)
interest = ($540,000) - ($250,187.42)
interest = $289,812.58
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