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).
To calculate the salary after 17 years of continuous compounding, we can use the formula for continuously compounded interest:
A = P * e^(rt)
Where:
A = final amount (salary after 17 years)
P = initial amount (salary 17 years ago)
e = base of the natural logarithm (approximately 2.71828)
r = interest rate per period (inflation rate)
t = number of periods (17 years)
First, convert the given salary to a continuously compounded principal amount by dividing it by e:
P = 18492 / e
Next, substitute the values into the formula:
A = (18492 / e) * e^(0.0231 * 17)
Simplifying the equation:
A = 18492 * e^(0.0231 * 17)
Using a calculator, we find:
A ≈ 32605.2541
Rounded to the nearest cent, the salary today would be $32,605.25.