You want to save for retirement. Assuming you are now 25 years old and you want to retire at age 55, you have 30 years to watch your investment grow. You decide to invest in the stock market, which has earned about 13% per year over the past 80 years and is expected to continue at this rate. You decide to invest $2,000 today. How much do you expect to have in 40 years?

Arnold and Helene would like to visit Austria in two years to celebrate their 25th wedding anniversary. Currently, the couple has saved $27,000, but they expect the trip to cost$31,000. If they put $27,000 in an account that earns 7% interest, compounded annually, will they be able to pay for the trip in two years?

Denzel needs a new car. At the dealership, he finds the car that he likes. The dealership gives him two payment options: 1. Pay $35,000 for the car today. 2. Pay$4,000 at the end of each quarter for three years. Assuming Denzel uses a discount rate of 12% (or 3% quarterly), determine which option gives him the lower cost.

GMG Studios plans to invest $60,000 at the end of each year for the next three years. There are three investment options available.$

$$\begin{matrix} & \text{Annual Rate} & \text{Interest Compounded} & \text{Period Invested}\\ \hline \text{Option 1} & \text{7$\\\%$} & \text{Annually} & \text{3 years}\\ \text{Option 2} & \text{9} & \text{Annually} & \text{3 years}\\ \text{Option 3} & \text{11} & \text{Annually} & \text{3 years}\\ \end{matrix}$$

$ Determine the accumulated investment amount by the end of the third year for each of the options.

The four actors below have just signed a contract to star in a dramatic movie about relationships among hospital doctors. Each person signs independent contracts with the following terms:

$$\begin{matrix} \text{ } & \text{Contract Terms} & \text{ }\\ \hline \text{ } & \text{Contract Amount} & \text{Payment Date}\\ \hline \text{Derek} & \text{$\$ 600,000$} & \text{2 years}\\ \text{Isabel} & \text{$640,000$} & \text{3 years}\\ \text{Meredith} & \text{$500,000$} & \text{Today}\\ \text{George} & \text{$500,000$} & \text{1 year}\\ \end{matrix}$$

Assuming an annual discount rate of 9%, which of the four actors is actually being paid the most?

Ronald has an investment opportunity that promises to pay him $55,000 in three years. H e could earn a 6% annual return investing his money elsewhere. What is the most he would be willing to invest today in this opportunity?

You are planning to save for retirement over the next 30 years. To do this, you will invest $750 per month in a stock account and$250 per month in a bond account. The return of the stock account is expected to be 10 percent, and the bond account will pay 6 percent. When you retire, you will combine your money into an account with a return of 5 percent. How much can you withdraw each month from your account assuming a 25-year withdrawal period?

Funding your retirement You plan to retire in exactly 20 years. Your goal is to create a fund that will allow you to receive $20,000 at the end of each year for the 30 years between retirement and death (a psychic told you that you would die exactly 30 years after you retire). You know that you will be able to earn$11 \%$per year during the 30 -year retirement period.

d. Now assume that you will earn$10 \%$from now through the end of your retirement. You want to make 20 end-of-year deposits into your retirement account that will fund the 30 -year stream of$\$20,000$ annual annuity payments. How large do your annual deposits have to be?

Complete the sentence in a way that shows you understand the meaning of the italicized vocabulary word. Displeased with the mayor's decision, several dissidents...

Which two Cold War events do you think had the greatest impact on the U.S. decision to pursue détente?

You want to invest $5000 in a certificate of deposit for 12 months. You are given the options below. Which would you choose? Explain.$r=4.75 %$, continuous compounding

Test the series $\sum_{n=1}^{\infty} \frac{n !}{2^{2 n}}$ for convergence or divergence and give a reason for your decision.

Test the series $\sum_{n=1}^{\infty} \frac{3^n n \text { ! }}{n^n}$ for convergence or divergence and give a reason for your decision.

The 2012 and the 2022 (projected) civilian labor forces by age are given in the following table.

$$\begin{array}{rrr} Age\ (in\ years) & 2012\ (in\ millions) & 2022\ (in\ millions) \\ \hline 16\ to\ 24 & 21.3 & 18.5 \\ 25\ to\ 54 & 101.3 & 103.2 \\ 55\ and\ over & 32.4 & 41.8 \\ \hline Total & 155 & 163.5 \\ \end{array}$$

(a) In 2012, find the probability that a member of the civilian labor force is age 55 or older. (b) In 2022, find the probability that a member of the civilian labor force is age 55 or over.
(c) What do these projections imply about the future civilian labor force?