# Contemporary Mathematics for Business and Consumers Third Edition

Contemporary Mathematics for Business and Consumers Third Edition By: Robert A. Brechner COPYRIGHT © 2003 by South-Western, a division of 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) 730 -2214 Fax (800) 730 -2215 http: //www. thomsonrights. com

Chapter 12 Annuities Copyright © 2003 by South-Western

Chapter 12, Annuities Section I Future Value of an Annuity: Ordinary and Annuity Due 12 -1 Calculating the future value of an ordinary annuity by using tables. 12 -2 Calculating the future value of an annuity due by using tables. 12 -3 (Optional) Calculating the future value of an ordinary annuity and an annuity due by formula.

Chapter 12, Annuities (Cont. ) Section II Present Value of an Annuity 12 -4 Calculating the present value of an ordinary annuity by using tables. 12 -5 Calculating the present value of an annuity due by using tables. 12 -6 (Optional) Calculating the present value of an ordinary annuity and an annuity due by formula.

Chapter 12, Annuities Section III Sinking Funds and Amortization 12 -7 Calculating the amount value of a sinking fund payment by table. 12 -8 Calculating the amount of an amortization by table an annuity by using table. 12 -9 (Optional) Calculating sinking fund payments by formula. 12 -10 (Optional) Calculating amortization payments by formula.

Section I, Future Value of an Annuity Ordinary and Annuity Due Steps for Calculating Future Value (amount) of an Ordinary Annuity Step 1. Calculate the interest rate period for the annuity (nominal rate / periods per year). Step 2. Determine the number of periods of the annuity (years x periods per year). Step 3. From Table 12 -1, locate the ordinary table factor at the intersection of the rate column and the periods row. Step 4. Calculate the future value of the ordinary annuity by using the formula. Future value = Ordinary table factor x Annuity payment

Everybody’s Business The procedure for using the annuity tables, Tables 12 -1 and 12 -2, is the same as we used the compound interest and present value tables in Chapter 11. Table factors are found at the intersection of the “rate period” column and the “number of periods” row.

12 -2 Calculating the Future Value of an Annuity Due by Using Tables Steps for Calculating Future Value (amount) of an Annuity Due: Step 1. Calculate the number of periods for the annuity (years x periods per year), and add one period to the total. Step 2. Calculate the interest rate period (nominal rate / periods per year). Step 3. From Table 12 -1, locate the ordinary table factor to get the annuity due table. Step 4. Calculate the future value of the annuity due table formula: Future value (annuity due) = Annuity table factor x Annuity payment

Everybody’s Business Note that the annuity due formula is the same as the ordinary annuity formula except it is multiplied by (1 + i). This is to account for the additional period of the annuity due.

Section II, Present Value of an Annuity 12 -4 Calculating the Present Value of an Ordinary Annuity by Using Tables Steps for Calculating Present Value of an Ordinary Annuity by Using Tables: Step 1. Calculate the interest rate period for the annuity (nominal rate / periods per year). Step 2. Determine the number of periods of the annuity (years x periods per year). Step 3. From Table 12 -2, locate the present value table factor at the intersection of the rate column and the periods row. Step 4. Calculate the present value of an ordinary annuity by using the formula: Present value = Annuity table factor x Annuity payment

Section II, Present Value of an Annuity 12 -4 Calculating the Present Value of an Ordinary Annuity by Using Tables Steps for Calculating Present Value of an Ordinary Annuity by Using Tables: Step 1. Calculate the interest rate period for the annuity (nominal rate / periods per year). Step 2. Determine the number of periods of the annuity (years x periods per year). Step 3. From Table 12 -2, locate the present value table factor at the intersection of the rate column and the periods row. Step 4. Calculate the present value of an ordinary annuity by using the formula: Present value = Annuity table factor x Annuity payment

12 -5 Calculating the Present Value of an Annuity Due by Using Tables Steps for Calculating Present Value of an Ordinary Annuity by Using Tables: Step 1. Calculate the number of periods for the annuity (years x periods per year), and subtract one period from the total. Step 2. Calculate the interest rate period (nominal rate / periods per year). Step 3. From Table 12 -2, locate the table factor at the intersection of the rate column and the periods row. Step 4. Add 1. 00000 to the ordinary annuity factor to get the annuity due table factor. Step 5. Calculate the present value of an annuity due by the formula: Present value = Ordinary annuity table factor x Annuity payment

Section III, Sinking Fund and Amortization n n 12 -7 Calculating the Amount Value of a Sinking Fund Payment by Table Steps for Calculating the Amount of a Sinking Fund Payment: Step 1. Using the appropriate rate period and number of periods of the sinking fund, find the future value table factor from Table 12 -1. Step 2. Calculate the amount of the sinking fund payment by Sinking fund payment = Future value of the sinking fund Future value table factor

12 -8 Calculating the Amount of an Amortization Payment by Table n Steps for Calculating the Amount of a Sinking Fund Payment: Step 1. Using the appropriate rate period and number of periods of the amortization, find the present value table factor from Table 12 -2. Step 2. Calculate the amount of the amortization fund payment by the formula Amortization payment = Original amount of obligation Present value table factor

Chapter 12, Annuities Annuity Complex annuity Contingent annuities Annuity due Present value of an annuity Amortization Simple annuity Annuities certain Ordinary annuity Future value of an annuity Sinking fund

Chapter 12 Future value(ordinary annuity) = Ordinary annuity table factor x Annuity payment FV(annuity due) = Annuity due table factor x Annuity payment Copyright © 2003 by South-Western

Chapter 12 Present value(ordinary annuity) = Ordinary annuity table factor x Annuity payment PV(annuity due) = Annuity due table factor x Annuity payment Copyright © 2003 by South-Western

Chapter 12 Sinking fund payment = Future value of the sinking fund Future value table factor Amortization payment = Original amount of obligation Present value table factor Copyright © 2003 by South-Western

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