$(4$ points$)$ Sam bought a house for $$150,000$ with some creative financing. The bank, which agreed to

lend Sam $$120,000$ for six years at $15\%$ interest, took a first mortgage on the house. The Joneses, who

sold Sam the house, agreed to lend him the remaining $$30,000$ for six years at $12\%$ interest. Thus Sam

became the owner without paying any cash at the beginning.

The first mortgage costs $$1,500$ a month and the second mortgage costs $$300$ a month. In both cases

these are "interest$-$only" loans: no principal is paid. The principal is due at the end of the loan. Sam rented

the house to a different couple. After receiving their monthly rent and paying other required costs $($taxes$,$

insurance, and so on$),$ he needed to pay $$1,000$ each month of his own money to cover the remainder of

the monthly mortgage payments.

At the end of three years, Sam sold the house for $$205,000.$ After paying off all costs $($such as the two

loans, real estate broker fees, and taxes$),$ he was left with $$40,000$ in revenue from the sale.

$($a$)$ Use interpolation to estimate the monthly rate of return Sam received on his investment $($rounded to

$2$ decimal places$).$ Identify the key numbers you need to include in these calculations and how you

would solve this, so that partial credit can be awarded if you aren't able to solve this.

$($b$)$ What effective annual rate of return did Sam receive on this investment $($rounded to $1$ decimal point$)?$

$($c$)$ Suppose that during the $3$ years that Sam made payments, the annual inflation rate was $5\%.$ What was

his real rate of return, adjusting for inflation? Round to $1$ decimal point again.