five years ago, william bought a twelve - room apartment complex for $340,000, and he plans to sell it…

five years ago, william bought a twelve - room apartment complex for $340,000, and he plans to sell it today. the real estate market caused williams complex to increase in value by 1.8% every year. william charges $525 per month to rent a room, and pays $36,500 in building upkeep every year. if william has kept all of his apartments continually rented out since he bought the building, to the nearest hundred dollars, how much profit will he realize once he sells it?\na. $195,500\nb. $227,200\nc. $226,100\nd. $245,500\nplease select the best answer from the choices provided

five years ago, william bought a twelve - room apartment complex for $340,000, and he plans to sell it today. the real estate market caused williams complex to increase in value by 1.8% every year. william charges $525 per month to rent a room, and pays $36,500 in building upkeep every year. if william has kept all of his apartments continually rented out since he bought the building, to the nearest hundred dollars, how much profit will he realize once he sells it?\na. $195,500\nb. $227,200\nc. $226,100\nd. $245,500\nplease select the best answer from the choices provided

Answer

Explanation:

Step1: Calculate the current value of the apartment complex

The formula for compound - interest is $A = P(1 + r)^t$, where $P$ is the principal amount, $r$ is the annual interest rate, and $t$ is the number of years. Here, $P=$340000$, $r = 0.018$, and $t = 5$. $A=340000\times(1 + 0.018)^5=340000\times1.018^5$ $1.018^5=1.018\times1.018\times1.018\times1.018\times1.018\approx1.0932$ $A = 340000\times1.0932=$371688$

Step2: Calculate the total rental income

There are 12 rooms, and the rent per room per month is $$525$. So the monthly rental income for 12 rooms is $12\times525=$6300$. The annual rental income is $6300\times12=$75600$. In 5 years, the total rental income is $75600\times5=$378000$

Step3: Calculate the total up - keep cost

The annual up - keep cost is $$36500$. In 5 years, the total up - keep cost is $36500\times5=$182500$

Step4: Calculate the profit

Profit=Current value of the complex+Total rental income - Total up - keep cost - Initial cost of the complex Profit=$371688 + 378000-182500 - 340000$ Profit=$371688+378000-(182500 + 340000)$ Profit=$749688 - 522500=$227188\approx$227200$

Answer:

B. $$227,200$