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Chapter 17: Q2. (page 369)

It is a fact that (1 + 0.12)3 = 1.40. Knowing that to be true, what is the present value of \(140 received in three years if the annual interest rate is 12 percent?

  1. \)1.40

  2. \(12

  3. \)100

  4. $112

Short Answer

Expert verified

Option (c) $100

Step by step solution

01

Step 1. Meaning and formula for the present value

The present value method says that the current value of the amount received in the future is the ratio of the future amount to the compound interest gained over the years.

X0=Xt1+it

X0 is the present value of the future amount, i is the interest rate, t is the time, and Xt is the amount received after t years.

02

Step 2. Calculations for the answer

Given that $140 will be received after 3 years along with the compound interest charged by 12% annually, the present value of $140 is:

X0=1401+0.123=1401.40=100

Hence, the answer is $100.

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Most popular questions from this chapter

Asset X is expected to deliver 3 future payments. They have present values of, respectively, \(1,000, \)2,000, and \(7,000. Asset Y is expected to deliver 10 future payments, each having a present value of \)1,000. 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.

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?

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?

Identify each of the following investments as either an economic investment or a financial investment.

a. A company builds a new factory.

b. A pension plan buys some Google stock.

c. A mining company sets up a new gold mine.

d. A woman buys a 100-year-old farmhouse in the countryside.

e. A man buys a newly built home in the city.

f. A company buys an old factory.

Suppose that the equation for the SLM is Y = 0.05 + 0.04X, where Y is the average expected rate of return, 0.05 is the vertical intercept, 0.04 is the slope, and X is the risk level as measured by beta. What is the risk-free interest rate for this SML? What is the average expected rate of return at a beta of 1.5? What is the value of beta at an average expected rate of return is 7 percent?
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