1950 AMC 12 Problem 23

Question

A man buys a house for

\$10{,}000

and rents it. He puts

12\dfrac12\%

of each month’s rent aside for repairs and upkeep; pays

\$325

a year taxes and realizes

5\dfrac12\%

on his investment. The monthly rent is:

\$64.82

\$83.33

\$72.08

\$45.83

\$177.08

Let

r

be the monthly rent and express the annual rent as

12r

After upkeep and taxes, the annual return must be

5.5\%

of

\$10,000

Let the monthly rent be

r

dollars. The yearly rent is

12r,

of which

1-0.125=\tfrac78

remains after setting aside the upkeep money. The desired yearly return is

0.055(10,000)=550

dollars, so

\frac78(12r)-325=550.

Hence

10.5r=875,

giving

r=83.\overline3,

which is

\$83.33

to the nearest cent.

Thus, the correct answer is B.

Problem 23 in other years