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You were hired by your employer 17 years ago. At the time, your salary was $18,492 per year. If your wage only went up due to inflation, how much would you make today, assuming continuous compounding? The inflation rate is 2.31%.
Round your answer to the nearest cent (hundedth).

Respuesta :

msm555

Answer:

$27386.17

Step-by-step explanation:

To calculate the future value of a salary with continuous compounding due to inflation, we can use the formula for continuous compound interest:

[tex]\sf A = P \cdot e^{rt} [/tex]

where:

  • [tex]\sf \bold{ A }[/tex] is the future value,
  • [tex]\sf \bold{ P }[/tex] is the present value (initial salary),
  • [tex]\sf \bold{ r }[/tex] is the annual inflation rate in decimal form,
  • [tex]\sf \bold{ t }[/tex] is the number of years.

In this case, we have:

  • [tex] \bold{ \sf P = \$18,492 }[/tex],
  • [tex]\sf \bold{\sf r = 0.0231 }[/tex] (2.31% expressed as a decimal), and
  • [tex]\sf \bold{\sf t = 17 }[/tex] years.

Substitute the given value:

[tex]\sf A = \$ 18492 \cdot e^{0.0231 \cdot 17} [/tex]

Now, calculate this value:

[tex]\sf A \approx \$ 18492 \cdot e^{0.3927} [/tex]

[tex]\sf A \approx \$ 18492 \cdot 1.48097403 [/tex]

[tex]\sf A \approx \$ 27386.17177 [/tex]

[tex]\sf A \approx \$27386.17 \textsf{(in nearest cent)}[/tex]

Therefore, if the wage only went up due to inflation over the 17 years, the salary today would be approximately $27386.17, rounded to the nearest cent.

semsee45

Answer:

$27,386.17

Step-by-step explanation:

To calculate the current salary based on continuous compounding inflation, we can use the continuous compounding interest formula:

[tex]\boxed{\begin{array}{l}\underline{\textsf{Continuous Compounding Interest Formula}}\\\\A=Pe^{rt}\\\\\textsf{where:}\\\phantom{ww}\bullet\;\;\textsf{$A$ is the final amount.}\\\phantom{ww}\bullet\;\;\textsf{$P$ is the principal amount.}\\\phantom{ww}\bullet\;\;\textsf{$e$ is Euler's number (constant).}\\\phantom{ww}\bullet\;\;\textsf{$r$ is the interest rate (in decimal form).}\\\phantom{ww}\bullet\;\;\textsf{$t$ is the time (in years).}\end{array}}[/tex]

Given that 17 years ago the salary was $18,492 per year, and the inflation rate is 2.31%, then:

  • P = $18,492
  • r = 2.31% = 0.0231
  • t = 17 years

Substitute these values into the equation:

[tex]A= 18492 \cdot e^{0.0231 \cdot 17}[/tex]

Now, solve for A:

[tex]\begin{aligned}A&= 18492 \cdot e^{0.3927}\\\\A&= 18492 \cdot 1.480974030...\\\\A&= 27386.17177144...\end{aligned}[/tex]

Round to the nearest hundredth:

[tex]A=27386.17[/tex]

Therefore, if the salary only increased due to inflation over the past 17 years, the current salary would be approximately $27,386.17 per year (rounded to the nearest cent).

[tex]\hrulefill[/tex]

Learn more about continuously compounding interest here:

https://brainly.com/question/44115700

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