Question

Luke earned 36,000 during the first year of his job at putt putt Kingdom. After each year he received a 10% raise find his total earnings during the first five years of the job.

Answer 1

Each year Luke earns the amount earned the previous year multiplied by 1.10 (which corresponds to a 10% raise).
The total earnings will be the sum of each year earnings.
This sum is given by the geometric series formula:
$S_{n} = \frac{ a_{1}(1 - r^{n}) }{1 - r}$

where:
a₁ = first term of the series
r = common ratio
n = number of term wanted

Therefore, the total earnings will be:
$S_{n} = \frac{ 36000(1 - 1.10^{5}) }{1 - 1.10}$
= 219783.60$

During the first five years of the job Luke earned 219783.60$.