G$\mathrm{.}1.$ A married couple want to buy a house priced at $$100,000$ and ask your advice. They would like to stay out of debt, so they plan on getting a long$-$term option to buy, and then saving up enough cash to pay for the house in one lump sum. They can save $$1,000$ per month in a

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PART TWO

Comparing Alternative Proposals

savings account that compounds interest at $0\mathrm{.}5$ percent per month compounded monthly. Meanwhile, due to inflation and increasing demand, the terms of the option provide that the price of the house will escalate $0\mathrm{.}5$ percent month.

$($a$)$ How long will it take before the amount in the savings account equals the rising price of the house?

$($b$)$ The couple now live in a trailer costing $$200$ per month, and if they bought the house now with no down payment and a $9$ percent mortgage, they could use the total $$1200(51000+$S$200)$ to pay off the mortgage. Which method pays for the house more quickly, $($a$)$ save up and pay cash, or $($b$)$ buy now, move in with nothing down, and pay off the mortgage at $$1200$ per month with a mortgage at $9$ percent $(0\mathrm{.}95\%/$month$)$

$($Ans$.$ buy now, n $=166$ months$)$