Chapter 13 - Annuities and sinking funds. The main contents of the chapter consist of the following: Annuities: ordinary annuity and annuity due (find future value), present value of an ordinary annuity (find present value), sinking funds (find periodic payments).
reached. Step 2. Add additional investment at the beginning of the period to the new balance Step 1. Calculate the interest on the balance for the period and add it to the previous balance 1312 Calculating Future Value of an Annuity Due Manually Find the value of an investment after 3 years for a $3,000 annuity due at 8% 1313 Manual Calculation $ 3,000.00 Beginning Yr 240.00 3,240.00 3,000.00 Beginning Yr 6,240.00 499.20 6,739.20 3,000.00 Beginning Yr 9,739.20 779.14 10,518.34 End of Yr Calculating Future Value of an Annuity Due by Table Lookup Step 4. Subtract 1 payment from Step 3. Step 3. Multiply the payment each period by the table factor. 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 1. Calculate the number of periods and rate per period. Add one extra period. 1314 Future Value of an Annuity Due Find the value of an investment after 3 years for a $3,000 annuity due at 8% N = 3 x 1 = 3 + 1 = 4 R = 8%/1 = 8% 4.5061 x $3,000 $13,518.30 $3,000 $10,518.30 1315 Calculating Present Value of an Ordinary Annuity by Table Lookup Step 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 of ordinary annuity pymt. Pymt. ordinary annuity table 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 1. Calculate the number of periods and rate per period 1316 Present Value of an Annuity John Fitch wants to receive a Interest ==> $8,000 annuity in 3 years. Interest on the annuity is 8% Payment ==> semiannually. John will make Interest ==> withdrawals at the end of each Payment ==> year. How much must John invest today to receive a stream of Interest ==> payments for 3 years N = 3 x 1 = 3 R = 8%/1 = 8% 2.5771 x $8,000 $20,616.80 1317 Payment ==> End of Year 3 ==> Manual Calculation $ 20,616.80 1,649.34 22,266.14 (8,000.00) 14,266.14 1,141.29 15,407.43 (8,000.00) 7,407.43 592.59 8,000.02 (8,000.00) 0.02 Lump Sums versus Annuities John 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? Future value of a lump sum N = 5 x 2 = 10 R = 8%/2 = 4% 12.0061 x $200 $2,401.22 Step 1 1318 Future value of an annuity N = 6 x 2 = 12 R = 8%/2 = 4% 1.6010 x $2,401.22 $3,844.35 Step 2 Lump Sums versus Annuities Mel Rich decided to retire in 8 years to New Mexico. What N = 8 x 1 = 8 amount must Mel invest today so R = 5%/1 = 5% he will be able to withdraw $40,000 at the end of each year 25 6768 x $563,756 years after he retires? Assume Mel can invest money at 5% $381,550.06 interest compounded annually Present value of a Step 2 lump sum N = 25 x 1 = 25 R = 5%/1 = 5% 14.0939 x $40,000 $563,756 1319 Present value of an annuity Step 1 Sinking Fund To 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 $1,314 x 45.5992 59,917.35* N = 18 x 1 = 18 N = 18, R= 10% R = 10%/1 = 10% Future Value of an annuity table 0.0219 x $60,000 $1,314 1320 Check * Off due to rounding ... an Annuity Due Manually Find the value of an investment after 3 years for a $3,000 annuity due at 8% 13 13 Manual Calculation $ 3,000.00 Beginning Yr 240.00 3,240.00 3,000.00 Beginning Yr 6,240.00 499.20... per period. Add one extra period. 13 14 Future Value of an Annuity Due Find the value of an investment after 3 years for a $3,000 annuity due at 8% N = 3 x 1 = 3 + 1 = 4 R = 8%/1 = 8% 4.5061 x $3,000 $13, 518.30 $3,000... end of each year? Use Table 13. 3 $1,314 x 45.5992 59,917.35* N = 18 x 1 = 18 N = 18, R= 10% R = 10%/1 = 10% Future Value of an annuity table 0.0219 x $60,000 $1,314 13 20 Check * Off due to rounding