you were hired by your employer 17 years ago. at the time, your salary was $18,492 per year. if your wage…

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 (hundredth)

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 (hundredth)

Answer

Explanation:

Step1: Identify the formula

The formula for continuous - compounding is $A = Pe^{rt}$, where $A$ is the final amount, $P$ is the principal amount, $r$ is the annual interest rate (inflation rate in this case), and $t$ is the time in years.

Step2: Identify the values of $P$, $r$, and $t$

$P=$18492$, $r = 0.0231$ (since $2.31%=0.0231$), and $t = 17$ years.

Step3: Substitute the values into the formula

$A=18492\times e^{0.0231\times17}$. First, calculate the exponent: $0.0231\times17 = 0.3927$. Then, find $e^{0.3927}$. Using a calculator, $e^{0.3927}\approx1.48197$. Now, multiply by $P$: $A = 18492\times1.48197$. $A\approx18492\times1.48197 = 27304.58924\approx27304.59$.

Answer:

$27304.59$