Roy gets a job at a lifeguard at a local swimming pool. His salary is \( £ 22000 \) a year and a \( 5 \% \) pay rise each year for the next 3 years. Work out Roy's salary after 3 years. Give your answer to the nearest pound.

To calculate Roy's salary after 3 years with a 5% pay rise each year, we can use the formula for compound interest: \[ A = P \times (1 + r)^n \] Where: - \( A \) is the final amount (Roy's salary after 3 years) - \( P \) is the principal amount (Roy's initial salary) - \( r \) is the annual interest rate (5% or 0.05) - \( n \) is the number of years (3 years) Given: - Roy's initial salary (\( P \)) = £22,000 - Annual interest rate (\( r \)) = 5% or 0.05 - Number of years (\( n \)) = 3 years Substitute the values into the formula and calculate Roy's salary after 3 years. Calculate the value by following steps: - step0: Calculate: \(22000\left(1+0.05\right)^{3}\) - step1: Add the numbers: \(22000\times 1.05^{3}\) - step2: Convert the expressions: \(22000\left(\frac{21}{20}\right)^{3}\) - step3: Evaluate the power: \(22000\times \frac{9261}{8000}\) - step4: Multiply: \(\frac{101871}{4}\) Roy's salary after 3 years with a 5% pay rise each year will be approximately £25,467.75. Rounding this to the nearest pound, Roy's salary after 3 years will be £25,468.