Answer: $36000
Step-by-step explanation:
Each year francesca earns a salary of 2% higher than her previous years salary. Without the 2% increase, she earns 100% of her previous salary each year. With an increase of 2%, she earns 100 + 2 = 102% of her previous salary each year. This is a geometric progression and the total amount that she earned in 5 years will be the sum of the first 5 terms of the geometric series.
The formula for the sum of n terms of a geometric series is
Sn = [a(r^n - 1)] / r - 1
Where
a is the first term of the series
n is the number of terms or years
r is the common ratio
In her first 5 years at this job, she earned a total of 187,345. This means that
n = 5
S5 = 187,345
r = 102/100 = 1.02
S5 = 187345 = [a(r^n - 1)] / 1.02 - 1
187345 = a × (1.1040808032 - 1) /0.02
187345× 0.02 = 0.1040808032a
a = 3746.9/0.1040808032
a =$35999.91
Francesca's salary in her 1st year at this job is approximately $36000
