Maximum and Minimum function equation of a mortgage word problem

[a6m0]

Hi,

I'm having trouble with the problem

"payment of R dollars per month pays off a mortgage loan of217.39R dollars in 25 years. You plan on buying a house. Assume thatyou must have a down payment of 10% of the house price and there is atransaction cost of 8% of the house price, both of which you can cover.Express the (maximum) house price you can afford as a function ofthe monthly mortgage payment, and the (minimum) monthly mortgagepayment required as a function of the house price"

The wording seems strange to me, and I honestly have no idea where to begin or how to start this question.

Can someone help point me in the right direction?

Thanks in advance

 

[HallsofIvy]

I suspect that the words "maximum" and "minimum" are in parentheses because they are not particularly relevant. You could, of course, buy a house at a lower price and pay it off earlier with the given monthly payment or pay a higher monthly payment for a given price, again paying it off earlier. They are simply asking for the "house price" and "monthly payment" as given by this formula for a span of 25 years.

You are told that "payment of R dollars per month pays off a mortgage loan of217.39R dollars in 25 years".

Now let the principle, the house price, be "P". You "must have a down payment of 10% of the house price and there is a transaction cost of 8% of the house price, both of which you can cover." The "transaction cost" has nothing to do with the loan. You pay 10% of P, 0.10P, leaving a loan of 0.90P. According to what you were told before, to pay that off in 25 years, at R dollars per month, you must have 0.90P= 217.39R.

"Express the (maximum) house price you can afford as a function of the monthly mortgage payment" means to write P as a function of R. Divide both sides of 0.90P= 217.39R by 0.90 to get P= 217.39R/0.90= 241.54R.

"Express the (minimum) monthly mortgage payment required as a function of the house price" means to write R as a function of P. Divide both sides of 0.90P= 217.39R by 217.39 to get R= 0.90P/217.39= 0.00414P.

 

[stapel]

"payment of R dollars per month pays off a mortgage loan of217.39R dollars in 25 years. You plan on buying a house. Assume thatyou must have a down payment of 10% of the house price and there is atransaction cost of 8% of the house price, both of which you can cover.Express the (maximum) house price you can afford as a function ofthe monthly mortgage payment, and the (minimum) monthly mortgagepayment required as a function of the house price"

The wording seems strange to me...

Which part, specifically, "seems strange" to you? You know what "payments", "per month", "loan", "years", etc, mean. We'll be glad to explain whichever terms are throwing you off, but we'll need you to clarify which one(s) you mean.

Thank you!