Question

Beth currently brings in an annual salary of $37,000 and anticipates a raise of 5% every year. What will her salary be in 14 years?
If necessary, round your answer to the nearest cent.

Answer 1

To calculate Beth's salary in 14 years with an annual raise of 5%, we can use the formula for compound interest, which can also be applied to salary increments:

\[
S = P (1 + r)^n
\]

Where:
- \(S\) = future salary
- \(P\) = current salary ($37,000)
- \(r\) = raise rate (5% or 0.05)
- \(n\) = number of years (14)

Plugging in the values we have:

\[
S = 37000 \times (1 + 0.05)^{14}
\]
\[
S = 37000 \times (1.05)^{14}
\]

Now, we calculate \((1.05)^{14}\):

\[
(1.05)^{14} \approx 1.979
\]

Now we can find her future salary:

\[
S \approx 37000 \times 1.979
\]
\[
S \approx 73123.30
\]

Thus, Beth's salary in 14 years will be approximately **$73,123.30**.