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?
$A=P(1+r)^3$
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 (1)
Calculate the total profit in the first year: 1 , 000/ m o n t h × 12 m o n t h s = $12 , 000 .
Apply the percentage increase for 4 years: 12000 × ( 1 + 0.06 ) 4 .
Calculate the profit in the fifth year: 12000 × ( 1.06 ) 4 = $15 , 149.72 .
The expected profit in the fifth year is $15 , 149.72 .
Explanation
Calculate the first year profit Korey expects to average $1,000 of profit each month in his first year. This means his total profit for the first year is $1,000/month * 12 months = $12,000. He expects his profits to increase by 6% each year for the next 4 years. We want to find his expected profit in the fifth year.
Set up the formula To calculate the profit in the fifth year, we need to apply the 6% increase four times to the first year's profit. This can be calculated using the formula: P 5 = P 1 ∗ ( 1 + r ) 4 where P 5 is the profit in the fifth year, P 1 is the profit in the first year, and r is the rate of increase (6% or 0.06).
Calculate the profit in the fifth year Plugging in the values, we get: P 5 = 12000 ∗ ( 1 + 0.06 ) 4 P 5 = 12000 ∗ ( 1.06 ) 4 P 5 = 12000 ∗ 1.26247696 P 5 = 15149.72352
State the final answer Therefore, Korey expects to make approximately $15,149.72 in profits in his fifth year of operation.
Examples
Understanding percentage growth is useful in many real-life situations. For example, if you invest money in a savings account or the stock market, you can use similar calculations to estimate how much your investment will grow over time. This helps you make informed decisions about your finances and plan for the future. Also, businesses use these calculations to forecast sales and profits, which is crucial for budgeting and strategic planning.
