For each investment situation, identify (a) the annual interest rate, (b) the length of the investment in years, ( c ) the periodic interest rate, and (d) the number of periods of the investment.

$9 \%$ compounded monthly for $5$ years

A magazine publisher offers two subscription plans. Plan A is a one-year subscription for $19.95. Plan B is a lifetime subscription (lasting indefinitely) for$149.

Based on your answer to part (a), which plan should the subscriber use? Explain.

If an investment is made with an interest rate r compounded monthly, how long will it take for the investment to triple?

You are planning for an early retirement. You would like to retire at age 40 and have enough money saved to be able to withdraw $220,000 per year for the next 30 years (based on family history, you think you will live to age 70). You plan to save by making 20 equal annual installments (from age 20 to age 40) into a fairly risky investment fund that you expect will earn 8% per year. You will leave the money in this fund until it is completely depleted when you are 70 years old.

Requirements

1. How much money must you accumulate by retirement to make your plan work? (Hint: Find the present value of the$220,000 withdrawals.)
2. How does this amount compare to the total amount you will withdraw from the investment during retirement? How can these numbers be so different?

What are the four main determinants of investment? How would a change in interest rates affect investment?

How long will it take an investment of $8000 to double if the investment earns interest at the rate of$8\%$ compounded continuously?

One cell phone company offers a plan that costs $29.99 and includes unlimited night and weekend minutes. Another company offers a plan that costs$19.99 and charges $0.35 per minute during nights and weekends. For what numbers of night and weekend minutes does the second company’s plan cost more than the first company’s plan?

Identify the following investment as an investment in either debt (D) securities or equity (E) securities.

______Certificate of deposit

An investment initially worth $1200 grows by$11.2 \%$per year. When will the investment be worth$5000?

Plan A: $40,000 invested for 3 years at 4.5%, compounded quarterly Plan B:$40,000 invested for 3 years at 4.4%, compounded continuously

$\textbf{\textcolor{#4257b2}{Critical Thinking}} \hspace{10pt}$ A painter can be paid in two ways.

$$\begin{align*} \text{Plan A} &:\ \text{\$500 plus \$19 per hour}\\ \text{Plan B} &:\ \text{\$24 per hour}\\ \end{align*}$$

Suppose the job takes $n$ hours. For what values of $n$ is Plan A better for the painter than Plan B?

Describe a calling plan that is always more expensive than BigPhone's plan from Exercise 2. Justify you example.

One cell phone company offers a plan that costs $\$ 29.99$ and includes unlimited night and weekend minutes. Another company offers a plan that costs $\$ 19.99$ and charges $\$ 0.35$ per minute during nights and weekends. For what numbers of night and weekend minutes does the second company's plan cost more than the Iirst company's plan?

An investment grows at a continuous 12% rate per year. In how many years will the value of the investment double?