6. The Smith family wants to make a home improvement that is expected to cost $1

Question

6. The Smith family wants to make a home improvement that is expected to cost $100,000. They want to fund as much of the cost as possible with a home equity loan, but can afford payments of only $800 per month. Their bank offers equity loans at 12% compounded monthly for a maximum term of 10 years. a. How much cash do they need as a down payment? ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ b. Their bank account pays 8% compounded quarterly. If they delay starting the project for two years, how much would they have to save each quarter to make the required down payment if the loan rate and estimated cost remains the same? ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Explanation / Answer

a)

PV = Pmt x ((1-((1+r/n)-nt )) / r)

Payment per period = $800

Interest Rate per period = 12%/12 = 1% (As compounded monthly)

Number of Compounding per year (n) = 12

t = 10 Years

$800 x ((1-(1 + 0.01)-40)/0.01 = $26,267.75

So, he will be able to get a loan of $26,267.15 and
down payment will be $100,000 - $26,267.75 = $73,732.25

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