Answer:
(a) $38,242.96
(b) $350,391.07
Step-by-step explanation:
You want the 10th year salary and the sum of earnings for 10 years if the salary is 32,000 in the first year and increases 2% per year.
Geometric sequence
The salary values form a geometric sequence with first term $32,000 and common ratio 1+0.02 = 1.02. The n-th term of the sequence is given by ...
an = a1(r^(n-1))
an = 32000(1.02^(n-1))
The sum of n terms is given by ...
Sn = a1(r^n -1)/(r -1)
Sn = 32000(1.02^n -1)/0.02
a) 10th year
The salary in the 10th year is ...
a10 = 32000(1.02^(10 -1)) = 38,242.96
The salary for the 10th year is $38,242.96.
b) Total
The total paid in 10 years is ...
S10 = 32000(1.02^10 -1)/0.02 = 350,391.07
The total salary over the 10-year period is $350,391.07.
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Additional comment
If each year's salary is rounded to the nearest cent, the total for 10 years will be $350,391.08.
