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Chapter 17: Q2. (page 368)

What is compound interest? How does it relate to the formula Xt = (1 + i)t X0? What is present value? How does it relate to the formula Xt/(1 + i)t = X0?

Short Answer

Expert verified

By the given formula, compound interest calculates the present value of money in the future when the interest is compounded.

The present value refers to the present-day value of the future returns or costs by the given formula.

Step by step solution

01

Step 1. Compound interest

Compound interest explains how quickly an investment increases in value when interest is compounded, not only on the original amount invested but also on all interest payments that have been previously made. In the given formula, Xt is the value of the initial investment after t years when the annual compound rate of interest is i.

02

Step 2. Present value 

Present value is the present-day value of returns or costs that are expected to arrive in the future. Present value is especially useful when investors wish to determine the proper current price to pay for an asset. The given equation says that Xt dollars in t years convert into exactly Xt/(1 + i)t dollars today.

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Most popular questions from this chapter

If the Fed increases interest rates, the SML will shift _______ and asset prices will _______.

  1. down; rise

  2. down; fall

  3. up; rise

  4. up; fall

If an investment has 35 percent more non-diversifiable risk than the market portfolio, its beta will be:

  1. 35

  2. 1.35

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Suppose that the city of New York issues bonds to raise money to pay for a new tunnel linking New Jersey and Manhattan. An investor named Susan buys one of the bonds on the same day that the city of New York pays a contractor for completing the first stage of construction. Is Susan making an economic or a financial investment? What about the city of New York?

Asset X is expected to deliver 3 future payments. They have present values of, respectively, 1,000,2,000, and 7,000.AssetYisexpectedtodeliver10futurepayments,eachhavingapresentvalueof1,000. Which of the following statements correctly describes the relationship between the current price of Asset X and the current price of Asset Y?

  1. Asset X and Asset Y should have the same current price.

  2. Asset X should have a higher current price than Asset Y.

  3. Asset X should have a lower current price than Asset Y.

An investment has a 50 percent chance of generating a 10 percent return and a 50 percent chance of generating a 16 percent return. What is the investment’s average expected rate of return?

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