PERFORMANCE OBJECTIVES

Annuities2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 1Contemporary Mathematics FOR BUSINESS AND CONSUMERS Brechner12CHAPTERPowerPoint Presentation by Heather Mann12PERFORMANCE OBJECTIVESSection I Future Value of an Annuity: Ordinary and Annuity Due12-1:Calculating the future value of an ordinary annuity by using tables12-2:Calculating the future value of an annuity due by using tables12-3:(Optional) Calculating the future value of an ordinary annuity and an annuity due by formula

Section II Present Value of an Annuity: Ordinary and Annuity Due12-4:Calculating the present value of an ordinary annuity by using tables12-5:Calculating the present value of an annuity due by using tables12-6:(Optional) Calculating the present value of an ordinary annuity and an annuity due by formula

22012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 1212PERFORMANCE OBJECTIVESSection III Sinking Funds and Amortization12-7:Calculating the amount of a sinking fund payment by table12-8: Calculating the amount of an amortization payment by table12-9: (Optional) Calculating sinking fund payments by formula12-10: (Optional) Calculating amortization payments by formula

32012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. continued1212Types of Annuities42012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. annuityPayment or receipt of equal amounts of money per period for a specified amount of time.simple annuityAnnuity in which the number of compounding periods per year coincides with the number of annuity payments per year.complex annuityAnnuity in which the annuity payments and compounding periods do not coincide.annuities certainAnnuities that have a specified number of time periods.contingent annuitiesAnnuities based on an uncertain time period, such as the life of a person.125EXHIBIT 12-1Timeline Illustrating Present and Future Value of an Annuity2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

12Annuity Payment Types62012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. ordinary annuityAnnuity that is paid or received at the end of each time period.annuity dueAnnuity that is paid or received at the beginning of each time period.future value of an annuityThe total amount of the annuity payments and the accumulated interest on those payments.Also known as the amount of an annuity.12Manually Calculating the Future Value of an Ordinary Annuity Example72012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. A bank is paying 8% interest compounded annually. Find the future value of $1,000 deposited at the end of every year for 3 years.Beginning of period 1 = 0First annuity payment = +1,000.00End of period 1 = 1,000.00Begin period 2 + second payment = 2,000.00I = PRT = 1,000 .08 1 = + 80.00End of period 2 = 2,080.00Begin period 3 + third payment = 3,080.00I = PRT = 2,080 .08 1 = + 166.40Future value of the ordinary annuity = 3,246.40128Step 1Calculate the interest rate per period for the annuity (nominal rate periods per year).Step 2Determine the number of periods of the annuity (years periods per year).Step 3From Table 12-1, locate the ordinary annuity table factor at the intersection of the rate-per-period column and the number-of-periods row.Step 4Calculate the future value of the ordinary annuity.

For calculating future value (amount) of an ordinary annuity2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Future value(ordinary annuity)=Ordinary annuitytable factorAnnuitypaymentSTEPS1289TABLE 12-1Future Value (Amount) of an Ordinary Annuity of $12012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

12Calculating the Future Value of an Ordinary Annuity Example102012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. A bank is paying 8% interest compounded annually. Find the future value of $1,000 deposited at the end of every year for 3 years.

Periods = 3 1 = 3 Interest rate per period = 8% 1 = 8% Future value = Table factor Annuity paymentFuture value = 3.24640 1,000 = $3,246.4012Manually Calculating the Future Value of an Annuity Due112012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. A bank is paying 6% interest compounded annually. Calculate the future value of $1,000, deposited at the beginning of each year for three years.Beginning of period 1 = 1,000.00I = PRT = 1,000 .06 1 = + 60.00End of period 1 = 1,060.00Beginning of period 2 (includes 2nd payment) = 2,060.00I = PRT = 2,060 .06 1 = 123.60) = + 123.60End of period 2 = 2,183.60Beginning of period 3 (includes 3rd payment) = 3,183.60I = PRT = 3,183.60 .06 1 = + 191.02End of period 3 = 3,374.621212Step 1Calculate the number of periods of the annuity (years periods per year) and add one period to the total.Step 2Calculate the interest rate per period (nominal rate periods per year).Step 3From Table 12-1, locate the table factor at the intersection of the rate-per-period column and the number-of-periods row.Step 4Subtract 1.00000 from the ordinary annuity table factor to get the annuity due table factor.Step 5Calculate the future value of the annuity due.Future value (annuity due) = Annuity due table factor Annuity paymentFor calculating future value (amount) of an annuity due2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. STEPS12Calculating the Future Value (Amount) of an Annuity Due Example132012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. A bank is paying 6% interest compounded annually. Calculate the future value of $1,000, deposited at the beginning of each year for 3 years.Interest rate per period = 6% 1 = 6%Periods: 3 1 = 3 + 1 = 4Table factor = 4.37462 1.0000 = 3.37462Future value = 3.37462 1,000 = 3,374.62/F = P*(1 + r)n

1214Step 1Calculate the interest rate per period for the annuity (nominal rate periods per year).Step 2Determine the number of periods of the annuity (years periods per year).Step 3From Table 12-2, locate the present value table factor at the intersection of the rate-per-period column and the number-of-periods row.Step 4Calculate the present value of the ordinary annuity.

For calculating present value of an ordinary annuity2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Present value(ordinary annuity)=Ordinary annuitytable factorAnnuitypaymentSTEPS121415TABLE 12-2Present Value (Amount) of an Ordinary Annuity of $12012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

12Calculating the Present Value of an Annuity Due162012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. A theater wants $20,000 available at the end of each 6-month theater season for renovations and new stage and lighting equipment. How much must be deposited now, at 8% compounded semiannually, to yield this annuity payment for the next 6 years?Interest per period = 8% 2 = 4%Periods = 6 2 = 12Present value = 9.38507 20,000 = $187,701.401217Step 1Calculate the number of periods of the annuity (years periods per year) and subtract one period from the total.Step 2Calculate the interest rate per period (nominal rate periods per year).Step 3From Table 12-2, locate the table factor at the intersection of the rate-per-period column and the number-of-periods row.Step 4Add 1.00000 from the ordinary annuity table factor to get the annuity due table factor.Step 5Calculate the future value of the annuity due.Present value (annuity due) = Annuity due table factor Annuity paymentFor calculating Present value of an annuity due2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. STEPS12Calculating the Present Value of an Annuity Due Example182012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Based on sales and revenue expense forecasts, it is estimated that $10,000 must be sent to the IRS for income tax purposes at the beginning of each 3-month period for the next 3 years. How much must be deposited now, at 6% compounded quarterly, to yield the annuity payment needed?Interest per period = 6% 4 = 1.5% Periods = 3 4 = 12 1 = 11Table factor = 10.07112 + 1.0000 = 11.07112Present value = 11.07112 10,000 = $110,711.201219Step 1Using the appropriate rate per period and number of periods of the sinking fund, find the future value table factor from Table 12-1.Step 2Calculate the amount of the sinking fund payment.

Sinking fund payment =For calculating the amount of a sinking fund payment2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Future value of the sinking fundFuture value table factorSTEPS12Calculating the Amount of a Sinking Fund Example202012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Steve wants to accumulate $8,000 in 5 years. If his bank is paying 12% interest compounded quarterly, how much must he deposit(payment) at the end of period to reach his desired goal?Interest per period: 12% 4 = 3%Periods = 5 4 = 20Sinking fund payment = Future value of the sinking fundFuture value table factorSinking fund payment =8,000 = $297.7326.870371221Step 1Using the appropriate rate per period and number of periods of the amortization, find the present value table factor from Table 12-2.Step 2Calculate the amount of the amortization payment.

Amortization payment =For calculating the amount of an amortization payment2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Original amount of obligationPresent value table factorSTEPS12Calculating the Amount of an Amortization Payment Example222012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. A fisherman purchases a new fishing boat for $130,000. He made a $20,000 down payment and financed the balance at his bank for 7 years. What amortization payments are required every 3 months, at 16% interest, to pay off the boat loan?Interest per period: 16% 4 = 4%Periods = 7 4 = 28Sinking fund payment = Original amount of obligationPresent value table factorSinking fund payment = 110,000 = $6,601.4316.6630612Chapter Review Problem 1232012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Jill has saved $200,000 and she wants to amortize (liquidate) that amount in a retirement fund so that she will receive equal annual payments over the next 25 years. At the end of the 25 years, there will be no funds left in the account. If the fund earns 12% interest, how much will Jill receive each year?

12Chapter Review Problem 2242012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Calculate the amount of the periodic payment needed to amount to $50,000 in 8 years compounded semi-annually at 10% interest.Interest per period: 10% 2 = 5%Periods = 8 2 = 16Sinking fund payment = Future value of the sinking fundFuture value table factorSinking fund payment =50,000 = $2,113.50 23.6574912Chapter Review Problem 3252012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. A bank is paying 6% interest compounded monthly. Find the future value of $100 deposited at the end of each month be worth after 2 years.

Periods = 2 12 = 24 Interest rate per period = 6% 12 = .5% Future value = 25.43196 100 = $2,543.2012