Henry and his new wife, meaghan, have disposable income of $192,000 per year. they can get a loan for 30 years at 3.5% apr. if they use this disposable income to purchase a home, what is the most expensive house they can afford?

They can afford a loan value of $1,781,560

Step-by-step explanation:

Generally, lenders like to see a family spend no more than 50% of their disposable income on debt service. If the home loan is the only debt Meaghan and Henry have, then they can afford a monthly payment of ...

... $192,000/12 × 50% = $8000

The loan amortization formula (or a calculator) can be used to find the corresponding loan principal amount, given the rate and time.

... A = P(r/n)/(1 -(1 +r/n)^(-nt)) . . . . for r=3.5%, n=12, t=30, A=8000

... $8000 = P(0.035/12)/(1 -(1 +.035/12)^(-12*30)) ≈ P(0.00449044688)

... P = $8000/0.00449044688) ≈ $1,781,559.88

This is the maximum amount Meaghan and Henry can finance, assuming no other debt. A typical home deal involves a down payment, and closing costs that may be over and above the price of the house. The most expensive house they can afford will depend on these other factors and the couple's ability to pay costs that are not financed (their savings or other sources of cash).

when functions are first introduced, you will probably have some simplistic "functions" and relations to deal with, usually being just sets of points. these won't be terribly useful or interesting functions and relations, but your text wants you to get the idea of what the domain and range of a function are. small sets of points are generally the simplest sorts of relations, so your book starts with those.

step-by-step explanation:

state the domain and range of the following relation. is the relation a function?

{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

the above list of points, being a relationship between certain x's and certain y's, is a relation. the domain is all the x-values, and the range is all the y-values. to give the domain and the range, i just list the values without duplication:

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

(it is customary to list these values in numerical order, but it is not required. sets are called "unordered lists", so you can list the numbers in any order you feel like. just don't duplicate: technically, repetitions are okay in sets, but most instructors would count off for this.)

while the given set does indeed represent a relation (because x's and y's are being related to each other), the set they gave me contains two points with the same x-value: (2, –3) and (2, 3). since x = 2 gives me two possible destinations (that is, two possible y-values), then this relation is not a function.

note that all i had to do to check whether the relation was a function was to look for duplicate x-values. if you find any duplicate x-values, then the different y-values mean that you do not have a function. remember: for a relation to be a function, each x-value has to go to one, and only one, y-value.

state the domain and range of the following relation. is the relation a function?

{(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}

i'll just list the x-values for the domain and the y-values for the range: