11. The Johnsons have accumulated a nest egg of $15,000 that they intend to use
ID: 2775869 • Letter: 1
Question
11. The Johnsons have accumulated a nest egg of $15,000 that they intend to use as a down payment toward the purchase of a new house. Because their present gross income has placed them in a relatively high tax bracket, they have decided to invest a minimum of $1300/month in monthly payments (to take advantage of the tax deduction) toward the purchase of their house. However, because of other financial obligations, their monthly payments should not exceed $1600.
A) If local mortgage rates are 8.5%/year compounded monthly for a conventional 30-year mortgage, what is the price range of houses they should consider? (Round your answers to the nearest cent.)
least expensive $
most expensive $
B) What If the Johnsons decide to secure a 15-year mortgage instead of a 30-year mortgage, what is the price range of houses they should consider when the local mortgage rate for this type of loan is 8%/year compounded monthly? (Round your answers to the nearest cent.)
least expensive $
most expensive $
Explanation / Answer
a is more expensive than b
a.We know that monthly payment can be made $1300
Number of months = 30 Years *12 = 360
Interest rate = 8.5% Yearly = 8.5% /12 = 0.00708 monthly
Down payment = $15000
Hence we can calculate the Present value of the total payments and that shall be value of the house they should consider
Present value formula =
PV = P*[{1- (1+r)^(-n)}/r]
Here
P = monthly payment = $1300
n = Number of months = 30 Years *12 = 360
r= Interest rate = 8.5% Yearly = 8.5% /12 = 0.00708monthly
Hence PV = 1300*[{1- (1+0.00708)^(-360)}/ 0.00708]
= 1300*[0.9211194/ 0.00708]
= 1300*130.10160
=$169132.0881
Price range of the House they should consider = 169132.0881 + 15000 = $1,184,132.0881
b.
We know that monthly payment can be made $1300
Number of months = 15 Years *12 = 180
Interest rate = 8% Yearly = 8 /12 = 0.00667monthly
Down payment = $15000
Hence we can calculate the Present value of the total payments and that shall be value of the house they should consider
Present value formula =
PV = P*[{1- (1+r)^(-n)}/r]
Here
P = monthly payment = $1300
n = Number of months = 15 Years *12 = 180
r= Interest rate = 9.5% Yearly = 9.5% /12 = 0.006667monthly
Hence PV = 1300*[{1- (1+0.006667)^(-180)}/ 0.006667]
= 1300*[0.697622/ 0.006667]
= 1300*104.63806
=$136029.4828
Price range of the House they should consider = 136029.4828 + 15000 = $1,51,029.4828
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