Question
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).
Round your answer to the nearest cent (hundedth).
Answers
GPT 3.5
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.
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.