/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q2. What is compound interest? How d... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

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.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Corporations often distribute profits to their shareholders in the form of dividends, which are quarterly payments sent to shareholders. Suppose that you have the chance to buy a share in a fashion company called Rogue Designs for \(35 and that the company will pay dividends of \)2 per year on that share. What is the annual percentage rate of return? Next, suppose that you and other investors could get a 12 percent per year rate of return on the stocks of other very similar fashion companies. If investors care only about rates of return, what should happen to the share price of Rogue Designs? (Hint: This is an arbitrage situation.)

Sammy buys stock in a suntan-lotion maker and also stock in an umbrella maker. One stock does well when the weather is good; the other does well when the weather is bad. Sammy鈥檚 portfolio indicates that 鈥渨eather risk鈥� is a _______ risk.

  1. diversifiable

  2. nondiversifiable

  3. automatic

Next, consider another pair of assets, C and D. Asset C will make a single payment of \(150 in one year while D will make a single payment of \)200 in one year. Assume that the current price of C is \(120 and that the current price of D is \)180.

c. What are the rates of return of assets C and D at their current prices? Given these rates of return, which asset should investors buy and which asset should they sell?

d. Assume that arbitrage continues until C and D have the same expected rate of return. When arbitrage ends, will C and D have the same price?

Compare your answers to questions a through d before answering question e.

e. We know that arbitrage will equalize rates of return. Does it also guarantee to equalize prices? In what situations will it equalize prices?

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

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.
See all solutions

Recommended explanations on Economics Textbooks

Taxation Economics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.