Yogajothi is thinking of investing in a rental house. The total cost to purchase the house,

including legal fees and taxes, is $$230000.$ All but $$30000$ of this amount will be

mortgaged. He will pay $$1600$ per month in mortgage payments. At the end of two years,

he will sell the house and at that time expects to clear $$40000$ after paying off the remaining

mortgage principal $($in other words, he will pay off all his debts for the house and still

have $$40000$ left$).$ Rents will earn him $$2000$ per month for the first year and $$2400$ per

month for the second year. The house is in fairly good condition now, so he doesn$$t expect

to have any maintenance costs for the first six months. For the seventh month, Yogajothi

has budgeted $$400.$ This figure will be increased by $$40$ per month thereafter $($e$.$g$.,$ the

expected month $7$ expense will be $$400,$ month $8,$ $$440,$ month $9,$ $$480,$ etc.$).$ If interest is

$6$ percent compounded monthly, what is the present worth of this investment? Given that

Yogajothi$$s estimates of revenue and expenses are correct, should he buy the house?