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Kehlani was offered a job that paid a salary of $44,000 in its first year. The salary was set to increase by 5% per year every year. If Kehlani worked at the job for 11 years, what was the total amount of money earned over the 11 years, to the nearest whole number? Answer:

Kehlani was offered a job that paid a salary of $44,000 \$ 44,000 in its first year. The salary was set to increase by 5% 5 \% per year every year. If Kehlani worked at the job for 1111 years, what was the total amount of money earned over the 1111 years, to the nearest whole number?\newlineAnswer:

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Q. Kehlani was offered a job that paid a salary of $44,000 \$ 44,000 in its first year. The salary was set to increase by 5% 5 \% per year every year. If Kehlani worked at the job for 1111 years, what was the total amount of money earned over the 1111 years, to the nearest whole number?\newlineAnswer:
  1. Determine Initial Salary: Determine the initial salary and the annual increase rate.\newlineKehlani's initial salary is $44,000\$44,000, and it increases by 5%5\% each year.
  2. Understand Salary Increase: Understand the nature of the salary increase.\newlineThe salary increase is a percentage of the previous year's salary, which means it's a geometric sequence.
  3. Calculate Salary for Each Year: Calculate the salary for each year and keep a running total.\newlineYear 11: $44,000\$44,000 (initial salary)\newlineYear 22: $44,000×1.05\$44,000 \times 1.05\newlineYear 33: $44,000×(1.05)2\$44,000 \times (1.05)^2\newline...\newlineYear 1111: $44,000×(1.05)10\$44,000 \times (1.05)^{10}
  4. Use Geometric Series Formula: Use the formula for the sum of a geometric series to find the total salary over 1111 years.\newlineThe sum SS of nn terms of a geometric series with first term aa and common ratio rr is given by S=a×(1−rn)/(1−r)S = a \times (1 - r^n) / (1 - r), where nn is the number of terms.\newlineHere, a=$(44,000)a = \$(44,000), r=1.05r = 1.05, and n=11n = 11.
  5. Substitute Values and Calculate: Substitute the values into the formula and calculate the sum.\newlineS=$44,000×(1−(1.05)11)/(1−1.05)S = \$44,000 \times (1 - (1.05)^{11}) / (1 - 1.05)
  6. Perform Calculations: Perform the calculations.\newlineS=$44,000×(1−(1.05)11)/(1−1.05)S = \$44,000 \times (1 - (1.05)^{11}) / (1 - 1.05)\newlineS=$44,000×(1−1.71034)/(−0.05)S = \$44,000 \times (1 - 1.71034) / (-0.05)\newlineS=$44,000×(−0.71034)/(−0.05)S = \$44,000 \times (-0.71034) / (-0.05)\newlineS=$44,000×14.2068S = \$44,000 \times 14.2068\newlineS=$624,099.20S = \$624,099.20
  7. Round Total Salary: Round the total salary to the nearest whole number.\newlineTotal salary over 1111 years = $624,099\$624,099

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