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1-2 Chapter 13 Annuities and Sinking Funds McGraw-Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved.

1-3 Differentiate between contingent annuities and annuities certain Calculate the future value of an ordinary annuity and an annuity due manually and by table lookup Annuities and Sinking Funds #13 Learning Unit Objectives Annuities: Ordinary Annuity and Annuity Due (Find Future Value) LU13.1

1-4 Calculate the present value of an ordinary annuity by table lookup and manually check the calculation Compare the calculation of the present value of one lump sum versus the present value of an ordinary annuity Annuities and Sinking Funds #13 Learning Unit Objectives Present Value of an Ordinary Annuity (Find Present Value) LU13.2

1-5 Calculate the payment made at the end of each period by table lookup Check table lookup by using ordinary annuity table Annuities and Sinking Funds #13 Learning Unit Objectives Sinking Funds (Find Periodic Payments LU13.3

1-6 Compounding Interest (Future Value) Term of the annuity - the time from the beginning of the first payment period to the end of the last payment period. Future value of annuity - the future dollar amount of a series of payments plus interest Present value of an annuity - the amount of money needed to invest today in order to receive a stream of payments for a given number of years in the future Annuity - A series of payments

1-7 End of period $1.00 $2.08 $3.25 Figure 13.1 Future value of an annuity of $1 at 8%

1-8 Classification of Annuities Contingent Annuities - have no fixed number of payments but depend on an uncertain event Annuities certain - have a specific stated number of payments Life Insurance payments Mortgage payments

1-9 Classification of Annuities Ordinary annuity - regular deposits/payments made at the end of the period Annuity due - regular deposits/payments made at the beginning of the period Jan. 31MonthlyJan. 1 June 30QuarterlyApril 1 Dec. 31SemiannuallyJuly 1 Dec. 31AnnuallyJan. 1

1-10 Step 1. Calculate the number of periods and rate per period Step 2. Lookup the periods and rate in an ordinary annuity table. The intersection gives the table factor for the future value of $1 Step 3. Multiply the payment each period by the table factor. This gives the future value of the annuity Calculating Future Value of an Ordinary Annuity by Table Lookup

1-11 Tools for Calculating Compound Interest Number of periods (N) Number of years times the number of times the interest is compounded per year Rate for each period (R) Annual interest rate divided by the number of times the interest is compounded per year If you compounded $100 each year for 3 years at 6% annually, semiannually, or quarterly What is N and R? Annually:3 x 1 = 3 Semiannually: 3 x 2 = 6 Quarterly:3 x 4 = 12 Annually:6% / 1 = 6% Semiannually: 6% / 2 = 3% Quarterly:6% / 4 = 1.5% Periods Rate

1-12 Table 13.1 Ordinary annuity table: Compound sum of an annuity of $1

1-13 N = 5 x 1 = 5 R = 9%/1 = 9% x $2,000 $11, Future Value of an Ordinary Annuity Find the value of an investment after 5 years for a $2,000 ordinary annuity at 9%

1-14 Calculating Future Value of an Annuity Due by Table Lookup Step 1. Calculate the number of periods and rate per period. Add one extra period. Step 2. Look up the periods and rate in an ordinary annuity table. The intersection gives the table factor for the future value of $1 Step 3. Multiply the payment each period by the table factor. Step 4. Subtract 1 payment from Step 3.

1-15 Future Value of an Annuity Due Find the value of an investment after 5 years for a $2,000 annuity due at 9% N = 5 x 1 = = 6 R = 9%/1 = 9% x $2,000 $15, $2,000 $13,046.60

1-16 End of period $.93 $1.78 $2.58 Figure Present value of an annuity of $1 at 8%

1-17 Calculating Present Value of an Ordinary Annuity by Table Lookup Step 1. Calculate the number of periods and rate per period Step 2. Look up the periods and rate in an ordinary annuity table. The intersection gives the table factor for the present value of $1 Step 3. Multiply the withdrawal for each period by the table factor. This gives the present value of an ordinary annuity

1-18 Table Present Value of an Annuity of $1

1-19 Present Value of an Annuity Duncan Harris wants to receive a $5,000 annuity in 5 years. Interest on the annuity is 8% semiannually. Duncan will make withdrawals at the end of each year. How much must Duncan invest today to receive a stream of payments for 5 years. N = 5 x 2 = 10 R = 8%/2 = 4% x $5,000 $40, Interest ==> Payment ==> End of Year 5 ==>

1-20 Lump Sums versus Annuities Karen Jones made deposits of $1,000 to Fleet Bank, which pays 6% interest compounded annually. After 4 years, Karen makes no more deposits. What will be the balance in the account 10 years after the last deposit N = 4 x 1 = 4 R = 6%/1 = 6% x $1,000 $4, N = 10 x 1 = 10 R = 6%/1 = 6% x $4, $7, Future value of an annuity Future value of a lump sum

1-21 Sinking Funds (Find Periodic Payments) Bonds Sinking Fund = Future x Sinking Fund Payment Value Table Factor Bonds

1-22 Table Sinking Fund Table Based on $1

1-23 Sinking Fund To retire a bond issue, Randolph Company needs $150,000 in 10 years. The interest rate is 8% compounded annually. What payment must Randolph Co. make at the end of each year to meet its obligation? N = 10 x 1 = 10 R = 8%/1 = 8% x $150,000 $10,350 Check $10,350 x ,936.30* * Off due to rounding N = 10, R= 8% Future Value of an annuity table