Contemporary Mathematics for Business and Consumers Third Edition By: Robert A. Brechner COPYRIGHT © 2003 by South-Western, a division of Thomson Learning. Thomson Learning TM is a trademark used herein under license. ALL RIGHTS RESERVED. No part of this work covered by the copyright hereon may be reproduced or used in any form or by any means–graphic, electronic, or mechanical, including photocopying, recording, taping, Web distribution or information storage and retrieval systems–without the written permission of the publisher. For permission to use material from this text or product, contact us by Tel (800) Fax (800)

Chapter 11 Compound Interest and Present Value Copyright © 2003 by South-Western

Chapter 11, Compound Interest and Present Value Section I Compound Interest – The Time Value of Money 11-1 Manually calculating compound amount (future value) and compound interest Computing compound amount (future value) and compound interest by using compound tables Creating compound interest table factors for periods beyond the table.

Chapter 11, Compound Interest and Present Value (Cont.) Section I Compound Interest – The Time Value of Money 11-4 Calculating annual percentage yield (APY) or effective interest rate Calculating compound amount (future value) by using the compound interest formula.

Chapter 11, Compound Interest and Present Value (Cont.) Section II Compound Interest – The Time Value of Money 11-6 Calculating the present value of a future amount by using present values tables Creating present value table factors for periods beyond the table (Optional) Calculating present value of a future amount by using the present value formula.

Section I, Compound Interest – The Time Value of Money 11-1 Manually Calculating Compound Amount (Future Value) and Compound Interest 11-2 Computing Compound Amount (Future Value) and Compound Interest by Using Compound Interest Tables Compound interest = Compound amount - Principal Compound amount (future value) = Table factor x Principal

Section I, Compound Interest – The Time Value of Money Cont.) Compound periods = Years x Periods per year Interest rates per period = Nominal rate Periods per year

Everybody’s Business When using the maturity value formula, MV = P (1+RT), the order of the operation is  Multiply rate times time  Add the 1  Multiply by the principal

11-2 Steps for Using Compound Interest Tables Step 1. Scan across the top row to find interest rate per period. Step 2 Look down that column to the row corresponding to the number of periods. Step 3. The table at the intersection of the rate per period column and the number of periods row is the future value of $1.00 at compound interest. Multiply the table factor by the principal to determine the compound amount.

11-3 Creating Compound Interest Table Factors for Periods Beyond the Table Steps for Creating New Compound Interest Table Factors: Step 1. For the stated interest rate per period, find the two table factors that represent half of the periods required. Step 2 Multiply the two table factors from Step 1 to form the new factor. Step 3. Round the new factor to five decimal places.

11-4 Calculating Annual Percentage Yield (APY) or Effective Interest Rate Annual Percentage Yield: Annual percentage yield (APY) = Total compound interest earned in 1 year Principal

11-5 (Optional) Calculating Compound Amount (Future Value) by Using the Compound Interest Formula Steps for Solving the Compound Interest Formula : Step 1. Add the 1 and the interest rate per period. Step 2 Raise the sum from Step 1 to the n th power, using the y x key on your calculator. Step 3. Multiply the principal, P, by the answer from Step 2.

Everybody’s Business Regulation DD of the Truth in Savings Law, enacted by Congress in 1993, requires banks and other depository institutions to fully disclose the terms of deposit accounts to consumers. The major provisions of the regulation require institutions to:  Provide consumer account holders with information about important terms of account including annual percentage yield.  Provide fee and other information on any periodic statement sent to consumers.  Use certain methods to determine the balance on which interest is calculated.  Comply with special requirements when advertising deposit accounts.

Section II, Present Value 11-6 Calculating the Present Value of a Future Amount by Using Present value Tables Steps for Solving the Compound Interest Formula : Step 1. Scan across the top row to fine the interest rate per period. Step 2 Look down that column to the row corresponding to the number of periods. Step 3. The table factor found at the intersection of the rate per period column and the number of periods row is the present value of $1.00 at the compound interest. Multiply the table factor by the compound amount to determine the present value. Present value = Table factor x Compound amount (FV)

Chapter 11 Compound interest = Compound amount - Principal Compounding periods = Years x Periods per year Compound amount = Table factor x Principal Copyright © 2003 by South-Western

Chapter 11 Compound amount = Principal(1 + interest) periods Present value = Table factor x Compound amount Copyright © 2003 by South-Western

Chapter 11, Section I As an incentive to attract savings deposits, most financial institutions today offer daily or even continuous compounding. This means that savings or passbook accounts, as well as CDs, earn interest compounded each day or even more frequently--continuously, such as every hour or even every minute. Let’s take a look at daily compounding. To calculate the compound amount, A, of an investment with daily compounding, use the compound interest formula, modified as follows:  Rate per period (daily) = Copyright © 2003 by South-Western (nominal interest rate, i, divided by 365)  Number of periods (days), n, = number of days of the investment. Business Decision Daily Compounding