At age 35, Cynthia earns her MBA and accepts a position as a vice president of an asphalt company. Assume that she will retire at the age of 65 , having received an annual salary of $\$ 105,000$, and that the interest rate is $8 \%$, compounded continuously.
a) What is the accumulated present value of her position?
b) What is the accumulated future value of her position?

Step 1 ：Cynthia earns an annual salary of $105,000, and she will retire in 30 years. The interest rate is 8%, compounded continuously.

Step 2 ：The present value (PV) of a future cash flow is the amount of money that would need to be invested currently, at a given rate of interest, to generate that cash flow in the future. The formula for calculating the present value is: \(PV = \frac{FV}{(1 + \frac{r}{n})^{nt}}\) where: FV = future value, r = interest rate, n = number of times interest applied per time period, t = number of time periods.

Step 3 ：In this case, Cynthia's annual salary is the future value (FV), the interest rate is 8% (or 0.08), and the time period is 30 years (from age 35 to 65). The interest is compounded continuously, so n is effectively infinity.

Step 4 ：The future value (FV) of a present cash flow is the amount of money that a current investment will grow to by a certain future date, at a specified rate of interest. The formula for calculating the future value is: \(FV = PV * (1 + \frac{r}{n})^{nt}\)

Step 5 ：In this case, we want to find the future value of Cynthia's annual salary over 30 years, at an interest rate of 8%.

Step 6 ：Using the formulas, we find that the accumulated present value of her position is approximately \$9525.39 and the accumulated future value of her position is approximately \$1157433.52.

Step 7 ：Final Answer: The accumulated present value of her position is \(\boxed{9525.39}\) and the accumulated future value of her position is \(\boxed{1157433.52}\).