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A young engineer wishes to buy a house but only can afford monthly payments of $500....

A young engineer wishes to buy a house but only can afford monthly payments of $500. Thirty-year loans are available at 12% interest compounded monthly. If she can make a $5,000 down payment, what is the price of the most expensive house that she can afford to purchase? Solve using annuities

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Expert Solution

Answer: $53,609

Explanation:

Given Annuity payment, P = $500,

Number of periods, n = 30 x 12 = 360,

12% interest is compounded monthly, hence rate per period, r= 12%/12 = 1% = 0.01

We need to find the present value of annuity payment, PV

PV = P [1- (1+r)-n/r]

       = 500[1-(1+0.01)-360]/0.01

      = $48609.16554

We can round off the value to $48,609

The engineer can make a down payment of $5,000.

Hence the price of the most expensive house that she can afford to purchase= $48,609 + $5,000

                                                                         = $53,609

keosha answered 1 year ago
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