korey is planning to open a comic - book store. in his first year of operation, korey expects to average…

korey is planning to open a comic - book store. in his first year of operation, korey expects to average $1,000 of profit each month. he then expects profits to increase by 6% each year for the next 4 years. how much does korey expect to make in profits in his fifth year of operation? $a = p(1 + r)^t$ a. $15,149.72 b. $16,058.71 c. $31,120.46 d. $32,987.69 please select the best answer from the choices provided

korey is planning to open a comic - book store. in his first year of operation, korey expects to average $1,000 of profit each month. he then expects profits to increase by 6% each year for the next 4 years. how much does korey expect to make in profits in his fifth year of operation? $a = p(1 + r)^t$ a. $15,149.72 b. $16,058.71 c. $31,120.46 d. $32,987.69 please select the best answer from the choices provided

Answer

Explanation:

Step1: Calculate the first - year profit

The first - year profit is $1000$ per month. So the annual profit $P$ in the first year is $1000\times12 = 12000$.

Step2: Identify the values of $r$ and $t$

The growth rate $r=0.06$ and the number of years from the first year to the fifth year $t = 4$.

Step3: Use the compound - growth formula

We use the formula $A = P(1 + r)^t$. Substitute $P = 12000$, $r=0.06$ and $t = 4$ into the formula: [ \begin{align*} A&=12000\times(1 + 0.06)^4\ &=12000\times(1.06)^4\ &=12000\times1.26247696\ &=15149.72352 \end{align*} ]

Answer:

A. $$15,149.72$