Salaries usually grow at a rate around $$ 2 \% $$ annually. If your starting salary is $$ \$ 41,600 $$, how much would you be making after 40 years with the company? You may assume continuous compounding.

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To determine your salary after 40 years with a continuous annual growth rate of $$2\%$$, we can use the formula for continuous compounding:

$$
A = P \times e^{rt}
$$

Where:
- $$A$$ is the amount of money accumulated after time $$t$$,
- $$P$$ is the principal amount (initial salary),
- $$r$$ is the annual interest rate (growth rate),
- $$t$$ is the time the money is invested for,
- $$e$$ is the base of the natural logarithm (approximately $$2.71828$$).

**Given:**
- Starting salary, $$P = \$41,600$$
- Annual growth rate, $$r = 0.02$$ (2%)
- Time, $$t = 40$$ years

**Plugging in the values:**

$$
A = 41,600 \times e^{0.02 \times 40} = 41,600 \times e^{0.8}
$$

First, calculate $$e^{0.8}$$:

$$
e^{0.8} \approx 2.22554
$$

Now, multiply this by the starting salary:

$$
A \approx 41,600 \times 2.22554 \approx 91,750.50
$$

**Final Answer:**

After 40 years, your salary would be approximately **\$91,751**.
After 40 years, your salary would be approximately \$91,751.

Salaries usually grow at a rate around
annually. If your starting salary is ,
how much would you be making after 40
years with the company? You may assume
continuous compounding.

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Salaries usually grow at a rate around annually. If your starting salary is , how much would you be making after 40 years with the company? You may assume continuous compounding.