Kinh tế học - Chapter 13: Annuities and sinking funds

Chapter 13Annuities and Sinking FundsDifferentiate between contingent annuities and annuities certainCalculate the future value of an ordinary annuity and an annuity due manually and by table lookupAnnuities and Sinking Funds#13Learning Unit ObjectivesAnnuities: Ordinary Annuity and Annuity Due (Find Future Value)LU13.1Calculate the present value of an ordinary annuity by table lookup and manually check the calculationCompare the calculation of the present value of one lump sum versus the present value of an ordinary annuityAnnuities and Sinking Funds#13Learning Unit ObjectivesPresent Value of an Ordinary Annuity (Find Present Value)LU13.2Calculate the payment made at the end of each period by table lookupCheck table lookup by using ordinary annuity tableAnnuities and Sinking Funds#13Learning Unit ObjectivesSinking Funds (Find Periodic PaymentsLU13.3Compounding 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 interestPresent 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 futureAnnuity - A series of paymentsClassification of AnnuitiesContingent Annuities - have no fixed number of payments but depend on an uncertain eventAnnuities certain - have a specific stated number of paymentsLife Insurance paymentsMortgage paymentsClassification of AnnuitiesOrdinary annuity - regular deposits/payments made at the end of the periodAnnuity due - regular deposits/payments made at the beginning of the periodJan. 31 Monthly Jan. 1June 30 Quarterly April 1Dec. 31 Semiannually July 1Dec. 31 Annually Jan. 1Step 1. For period 1, no interest calculation is necessary, since money is invested at the end of period Step 2. For period 2, calculate interest on the balance and add the interest to the previous balance. Step 3. Add the additional investment at the end of period 2 to the new balance. Calculating Future Value of an Ordinary Annuity ManuallyStep 4. Repeat steps 2 and 3 until the endof the desired period is reached.Calculating Future Value of an Ordinary Annuity ManuallyFind the value of an investment after 3 years for a $3,000 ordinary annuity at 8%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.Future value of = Annuity pymt. x Ordinary annuityordinary annuity each period table factor Calculating Future Value of an Ordinary Annuity by Table LookupN = 3 x 1 = 3R = 8%/1 = 8%3.2464 x $3,000$9,739.20Future Value of an Ordinary AnnuityFind the value of an investment after 3 years for a $3,000 ordinary annuity at 8%Calculating Future Value of an Annuity Due ManuallyStep 1. Calculate the interest on the balance for the period and add it to the previous balance Step 2. Add additional investment at the beginning of the period to the new balance.Step 3. Repeat steps 1 and 2 until the end of the desired period is reached. Calculating Future Value of an Annuity Due ManuallyFind the value of an investment after 3 years for a $3,000 annuity due at 8%Calculating Future Value of an Annuity Due by Table LookupStep 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 $1Step 3. Multiply the payment each period by the table factor. Step 4. Subtract 1 payment from Step 3. Future Value of an Annuity DueFind the value of an investment after 3 years for a $3,000 annuity due at 8%N = 3 x 1 = 3 + 1 = 4R = 8%/1 = 8%4.5061 x $3,000$13,518.30 - $3,000$10,518.30Calculating Present Value of an Ordinary Annuity by Table LookupStep 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 $1Step 3. Multiply the withdrawal for each period by the table factor. This gives the present value of an ordinary annuity Present value of = Annuity x Present value ofordinary annuity pymt. Pymt. ordinary annuity tablePresent Value of an AnnuityJohn Fitch wants to receive a $8,000 annuity in 3 years. Interest on the annuity is 8% semiannually. John will make withdrawals at the end of each year. How much must John invest today to receive a stream of payments for 3 years.N = 3 x 1 = 3R = 8%/1 = 8%2.5771 x $8,000$20,616.80Interest ==>Payment ==>End of Year 3 ==>Interest ==>Interest ==>Payment ==>Payment ==>Lump Sums versus AnnuitiesJohn Sands made deposits of $200 to Floor Bank, which pays 8% interest compounded annually. After 5 years, John makes no more deposits. What will be the balance in the account 6 years after the last deposit?N = 5 x 2 = 10 R = 8%/2 = 4%12.0061 x $200$2,401.22 N = 6 x 2 = 12R = 8%/2 = 4%1.6010 x $2,401.22$3,844.35Future value of an annuityFuture value of a lump sumStep 1Step 2Lump Sums versus AnnuitiesMel Rich decided to retire in 8 years to New Mexico. What amount must Mel invest today so he will be able to withdraw $40,000 at the end of each year 25 years after he retires? Assume Mel can invest money at 5% interest compounded annually.N = 25 x 1 = 25 R = 5%/1 = 5%14.0939 x $40,000$563,756 N = 8 x 1 = 8R = 5%/1 = 5%.6768 x $563,756 $381,550.06Present value of an annuityPresent value of a lump sumStep 1Step 2Sinking FundTo retire a bond issue, Moore Company needs $60,000 in 18 years from today. The interest rate is 10% compounded annually. What payment must Moore make at the end of each year? Use Table 13.3.N = 18 x 1 = 18R = 10%/1 = 10%0.0219 x $60,000$1,314Check$1,314 x 45.599259,917.35** Off due to roundingN = 18, R= 10%Future Value of an annuity table