Part $2$

Buying the house

$$ The car down payment will come from their bank account, and whatever is left will stay in the checking account as a cash reserve.

$$ After all their other monthly expenses, G&M have a net positive cash flow of $$1500$ per month. They will make the monthly car payment, insurance payments, gas and oil payments from their cash flow of $$1500.$ Their current apartment rent does not come from this amount.

$$ Any excess cash $($from the $$1500)$ each month will go into a long term savings plan for $4$ years that pays an APR of $5\mathrm{.}5\%$ compounded monthly.

$$ At the end of the four years, they will keep the car if they have bought it$,$ or return the car to the dealership if they have leased it$.$ They will cash out the long term savings plan, put the amount of their original car down payment back in checking $($from their long$-$term savings$)$ so they can shop for a new car if they leased the car or save it to shop for a new car later if they bought the car.

$$ The remaining long term savings plan balance they will use as a down payment on a new house, which they expect to be $15\%$ of the house$$s price.

Calculate:

$1.$ Total funds in the long term savings plan after $4$ years,

$2.$ Funds available for a down payment on a house,

$3.$ Highest house price they can afford, and

$4.$ Monthly payment for a $30-$year mortgage at $3\mathrm{.}5\%$ APR for this highest option. You do not need to worry about the $$1500$ used to determine what could be put into a long term savings plan when computing the highest house price they could afford. Their past rent was not part of the $$1500.$