Sam is planning to start a pool cleaning business with an initial profit goal of $45,000 the first year. The annual profit is expected to increase by \(5.5\%\).
To calculate the profit for the third year, we can use the formula for compound interest which is:
[tex]\[ A = P(1 + r)^n \][/tex]
Here:
- \( P \) is the initial amount (initial profit), which is $45,000.
- \( r \) is the annual increase rate, which is \(5.5\%\) or \(0.055\) as a decimal.
- \( n \) is the number of years, which is 2 years (from the first year to the third year).
Plug these values into the formula:
[tex]\[ A = 45000 \times (1 + 0.055)^2 \][/tex]
First, calculate \(1 + 0.055\):
[tex]\[ 1 + 0.055 = 1.055 \][/tex]
Next, raise this value to the power of 2:
[tex]\[ 1.055^2 \approx 1.113 \][/tex]
Finally, multiply this by the initial profit:
[tex]\[ A = 45000 \times 1.113 \approx 50086.13 \][/tex]
Therefore, the expected profit for the third year is approximately $50,086.13.
The best answer from the choices provided is:
b. \$50,086.13
