The Johnsons have accumulated a nest egg of $50,000 that they intend to use as a
ID: 2525067 • Letter: T
Question
The Johnsons have accumulated a nest egg of $50,000 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 $2300/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 $2900. If local mortgage rates are 2.5%/year compounded monthly for a conventional 30-year mortgage, what is the price range of houses that they should consider? (Round your answers to the nearest cent.)
Explanation / Answer
Present Value of the monthly payments discounted at 2.5%(yearly) Compounded monthly.
If Present Value of $2300 per month Payment :-
= $2300 * Present Value of Annuity*
= $2300 * 253.09
= $582107
*Present Value of Annuity calculate in online Calculator
If Present Value of $2900 per month Payment :-
= $2900 * 253.09
= $733961
Apart from the loan, they have $50000 with them
Range of houses that they can consider
Least Expensive = $582107 + $50000 = $632107
Most Expensive = $733961 + $50000 = $783961
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