Say that you purchase an apartment complex for $655,000. the property value increases by 2.6% every year. the complex has five units, which you rent out for $490 per month. upkeep on the building costs you $13,800 per year. assuming that you are able to keep all of the units rented out constantly, after eight years, will you have gained more money from appreciation of the property or from renting out the apartments, and how much more money will you have gained from that source than from the other, to the nearest hundred dollars?
a.
you will gain $19,500 more from the rent than from the appreciation.
b.
you will gain $16,900 more from the rent than from the appreciation.
c.
you will gain $24,500 more from the appreciation than from the rent.
d.
you will gain $10,700 more from the appreciation than from the rent.

the answer is c

c.  You will gain $24,500 more from the appreciation than from the rent.

Step-by-step explanation:

To calculate this, compare the increase in value of the property and the net income from rent for the period (i.e. 8 years)

1. To Calculate Increase or Appreciation in Value of the Property  

FORMULA

             A  = (P( 1 + r )^n) - P

Where:  A  = Appreciation in Value of the Property

             P  =  Initial cost of the property =  $655,000

             n  = Number of years = 8 years

             r   = Annual growth rate of property = 2.6%

             A  = (P( 1 + r )^n) - P

                  = ($655,000( 1 + 2.6%)^8) -$655,000

                  = ($655,000( 1 . 026)^8) -$655,000

                  = $804,304 - $655,000

                  = $149,304

2. Net Income from Property  Rent for the Period

Number of units                = 5

Number of years              = 8

Rent income per month  = $490

Rent income per year      =  $490 x 5 x 12 = $29,400 (The complex is 5 units)

Rent income for 8 years  = $235,200       ($29,400 x 8)

Upkeep of building          =  $110.400         ($13,800 x 8)

Net Income from rent      =$ 124,800    

Increase in property value =  $149,304

Net Income from rent        =  $124,800

Difference                           =   $24,504

to the nearest hundred dollars? is $24,500

This means that you will gain $24,500 more from the appreciation than from the rent.

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11