korey is planning to open a comic - book store. his store will cost $12,500 to open and will come with a…

korey is planning to open a comic - book store. his store will cost $12,500 to open and will come with a $8,000 total annual operational cost. if his store makes $12,000 in profit during the first year, and profits increase by 6% each year from then, how long will it take for korey to see an overall profit in his business (where total profits exceed total expenses)? $a = p(1 + r)^t$ a. korey will see an overall profit in his first year of business. b. korey will see an overall profit in his second year of business. c. korey will see an overall profit in his third year of business. d. korey will see an overall profit in his fourth year of business. please select the best answer from the choices provided

korey is planning to open a comic - book store. his store will cost $12,500 to open and will come with a $8,000 total annual operational cost. if his store makes $12,000 in profit during the first year, and profits increase by 6% each year from then, how long will it take for korey to see an overall profit in his business (where total profits exceed total expenses)? $a = p(1 + r)^t$ a. korey will see an overall profit in his first year of business. b. korey will see an overall profit in his second year of business. c. korey will see an overall profit in his third year of business. d. korey will see an overall profit in his fourth year of business. please select the best answer from the choices provided

Answer

Explanation:

Step1: Calculate total initial expenses

The cost to open the store is $12500$ and the annual operational cost is $8000$. So the total initial - expense $E_0=12500$.

Step2: Calculate profit in the first year

The profit in the first year $P_1 = 12000$. The remaining expense after the first - year profit is $E_1=12500 - 12000=500$.

Step3: Calculate profit in the second year

Use the compound - growth formula $A = P(1 + r)^t$, where $P = 12000$, $r=0.06$, and $t = 1$. So the profit in the second year $P_2=12000\times(1 + 0.06)=12000\times1.06 = 12720$. The total profit after two years is $P_{total2}=12000 + 12720=24720$, and the total expense after two years is $12500+8000\times2=12500 + 16000=28500$. The remaining expense after the second - year profit is $E_2=28500 - 24720 = 3780$.

Step4: Calculate profit in the third year

$P_3=12720\times(1 + 0.06)=12720\times1.06=13483.2$. The total profit after three years is $P_{total3}=12000 + 12720+13483.2=38203.2$, and the total expense after three years is $12500+8000\times3=12500 + 24000=36500$. Since $38203.2>36500$.

Answer:

C. Korey will see an overall profit in his third year of business.