Question

Layla was offered a job that paid a salary of $52,000 in its first year. The salary was set to increase by 2% per year every year. If Layla worked at the job for 16 years, what was the total amount of money earned over the 16 years, to the nearest whole number?

Answer 1

$969,243 (nearest whole number)

Explanation:

Use geometric sum formula:

`S_n=(a(1-r^n))/(1-r)`

where
`a` is the initial value and
`r` is the common ratio

We have been told that the initial value is 52000, so
`a=52000`.

If Layla's salary increases by 2% per year, this means it is 102% of the previous year's salary. 102% = 102/100 = 1.02. Therefore,
`r = 1.02`

We need to calculate the sum of money earned over 16 years, so
`n = 16`

Inputting these values into the formula:

`\implies S_(16)=(52000(1-1.02^(16)))/(1-1.02)=\$969,243 \ \textsf{(nearest whole number)}`