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Nabhitha was offered a job that paid a salary of $83,000 in its first year. The salary was set to increase by 5% per year every year. If Nabhitha worked at the job for 26 years, what was the total amount of money earned over the 26 years, to the nearest whole number? Answer:

Nabhitha was offered a job that paid a salary of $83,000 \$ 83,000 in its first year. The salary was set to increase by 5% 5 \% per year every year. If Nabhitha worked at the job for 2626 years, what was the total amount of money earned over the 2626 years, to the nearest whole number?\newlineAnswer:

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Q. Nabhitha was offered a job that paid a salary of $83,000 \$ 83,000 in its first year. The salary was set to increase by 5% 5 \% per year every year. If Nabhitha worked at the job for 2626 years, what was the total amount of money earned over the 2626 years, to the nearest whole number?\newlineAnswer:
  1. Identify initial salary: Identify the initial salary and the annual increase percentage.\newlineNabhitha's initial salary is $83,000\$83,000, and it increases by 5%5\% each year.
  2. Determine formula for total salary: Determine the formula to calculate the total salary over 2626 years.\newlineThe salary increases exponentially, so we use the formula for the sum of a geometric series: Sn=a×(1−rn)/(1−r)S_n = a \times (1 - r^n) / (1 - r), where aa is the first term, rr is the common ratio, and nn is the number of terms.
  3. Calculate common ratio: Calculate the common ratio rr based on the annual increase.\newlineThe salary increases by 5%5\% each year, so the common ratio rr is 1+5100=1.051 + \frac{5}{100} = 1.05.
  4. Apply geometric series formula: Apply the formula for the sum of a geometric series to calculate the total salary.\newlineUsing the formula Sn=a×(1−rn)/(1−r)S_n = a \times (1 - r^n) / (1 - r), we substitute a=$83,000a = \$83,000, r=1.05r = 1.05, and n=26n = 26.\newlineS26=83,000×(1−1.0526)/(1−1.05)S_{26} = 83,000 \times (1 - 1.05^{26}) / (1 - 1.05)
  5. Calculate total salary: Calculate the total salary over 2626 years.\newlineS26=83,000×(1−1.0526)/(1−1.05)S_{26} = 83,000 \times (1 - 1.05^{26}) / (1 - 1.05)\newlineS26=83,000×(1−1.0526)/(−0.05)S_{26} = 83,000 \times (1 - 1.05^{26}) / (-0.05)\newlineS26=83,000×(1−4.291870)/(−0.05)S_{26} = 83,000 \times (1 - 4.291870) / (-0.05)\newlineS26=83,000×(−3.291870)/(−0.05)S_{26} = 83,000 \times (-3.291870) / (-0.05)\newlineS26=83,000×65.8374S_{26} = 83,000 \times 65.8374\newlineS26=5,464,442.2S_{26} = 5,464,442.2
  6. Round total salary: Round the total salary to the nearest whole number.\newlineThe total salary over 2626 years, rounded to the nearest whole number, is $5,464,442\$5,464,442.

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