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Question 1126389: The monthly payment p on a mortgage varies directly with the amount borrowed B. If the monthly payment on a 30 year mortgage is $5.75 for every $1000 borrowed, find a function p=p(B) that relates the monthly payment p to the amount borrowed B for a mortgage with the same terms. Then find the monthly payment p when the amount borrowed B is $225,000.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if it varies directly, then y = k * x.
k is the constant of variation.
first you solve for k and then you solve the problem.
you are given that the monthly payment on a 30 year mortgage is 5.75 for every 1000.
you are told that the monthly payment varies directly with the amount borrowed.
y = k * x is the formula for direct variation.
let y represent the monthly payment anbd x represent the amount borrwed.
the formula becomes 5.75 = k * 1000
solve for k to get k = 5.75 / 1000 = .00575.
that's your constant of variation.
when the amount borrowed is 225,000, then the formula of y = k * x becomes y = .00575 * 225,000.
solve for y to get y = 1293.75.
when the amount borrowed is 225,000, the monthly payment becomes 1293.75.
all other factors in the loan have to be the same, like the number of time periods and the interest rate per time period.
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