Time Value of Money, Part 4 Future Value aueof An Annuity Intermediate Accounting I Dr. Chula King 1 Learning Outcomes The concept of future value Future value of an annuity Ordinary annuity versus annuity due How to set up the problem How to use the tables to solve the problem. 2 Future Value Refers to the amount of money to which an investment will grow over a finite period of time at a given interest rate The cash value of an investment at a particular time in the future. 3 1
Annuity Equal periodic amount 1/1/1 1/1/2 1/1/3 1/1/4 10,000 10,000 10,000 10,000 1/1/1 1/1/2 1/1/3 1/1/4 10,000 12,000 15,000 10,000 1/1/1 7/1/1 7/1/2 10/1/2 10,000 10,000 10,000 10,000 4 Future Value of an Annuity Future value of an annuity determines the annuity value at a future time Types of annuity Ordinary Annuity An annuity whose deposits occur at the end of each period; determines the future value immediately after the last deposit. Annuity Due An annuity whose deposits occur at the beginning of each period; determines the future value one period after the last deposit. 5 Future Value of an Ordinary Annuity An annuity whose deposits occur at the end of each period... 0 1 2 3 Immediately after the last deposit 6 2
Example What is the future value of a three year ordinary annuity of 100 at 10% compounded annually? 7 A Pictorial Representation 0 1 2 3 x 1.10 + 110 210 x 1.10 + 231 331 Immediately after the last deposit 8 Table Solution Time value of money tables 1: Future value of a single sum 2: Present value of a single sum 3: Future value of an ordinary annuity 4: Present value of an ordinary annuity 5: Future value of an annuity due 6: Present value of an annuity due 9 3
Reading the Table Select the correct table (OA: 1.0000; AD: 1+ Interest) Select the column corresponding to the interest rate per period Read down that column to the row that corresponds to the number of deposits Take the resultant factor, and multiply it by the annuity amount The result is the future value of an ordinary annuity or annuity due! 10 Example What is the future value of a three year ordinary annuity of 100 at 10% compounded annually? 11 Future Value of An Ordinary Annuity (n=3, i=10%) n = # Deposits Immediately after the last deposit 12 4
Future Value of an Ordinary Annuity of $1 (n) i Periods 2% 4% 6% 8% 10% 1 1.00000 1.00000 1.00000 1.00000 1.00000 2 2.02000 2.04000 2.06000 2.08000 2.10000 3 3.06040 3.12160 3.18360 3.24640 3.31000 4 4.12161 4.24646 4.37462 4.50611 4.64100 5 5.20404 5.41632 5.63709 5.86660 6.10510 6 6.30812 6.63298 6.97532 7.33592 7.71561 13 Future Value of An Ordinary Annuity (n=3, i=10%) 3.3100 x 100 = 331.00 n = # Deposits Immediately after the last deposit 14 Example Amos Adams is 60 years old today. When he retires in five years at the age of 65, he would like to have $100,000 available to supplement his social security. Beginning on his 61 st birthday, Amos plans to make five equal annual deposits in a fund that earns 6% compounded annually. How much must each deposit be? 15 5
Pictorial Representation of Example.60 61 62 63 64 65 100,000 (n=5, i=6%) 16 Future Value of an Ordinary Annuity of $1 (n) i Periods 2% 4% 6% 8% 10% 1 1.00000 1.00000 1.00000 1.00000 1.00000 2 2.02000 2.04000 2.06000 2.08000 2.10000 3 3.06040 3.12160 3.18360 3.24640 3.31000 4 4.12161 4.24646 4.37462 4.50611 4.64100 5 5.20404 5.41632 5.63709 5.86660 6.10510 6 6.30812 6.63298 6.97532 7.33592 7.71561 17 The Solution.60 61 62 63 64 65 100,000 (n=5, i=6%) x 5.63709 = 100,000 = 100,000 5.63709 = $17,740 18 6
Future Value of an Annuity Due An annuity whose deposits occur at the beginning of each period. The future value is determined one period after the last deposit. 19 Example What is the value of a three year annuity due of 100 at 10% compounded annually? 20 The Solution (Table 5, n=3, i=10%) 21 7
Future Value of an Annuity Due of $1 (n) i Periods 2% 4% 6% 8% 10% 1 10200 1.0200 10400 1.0400 1.0600 1.0800 1.10001000 2 2.0604 2.1216 2.1836 2.2464 2.3100 3 3.1216 3.2465 3.3746 3.5061 3.6410 4 4.2040 4.4163 4.6371 4.8666 5.1051 5 5.3081 5.6330 5.9753 6.3359 6.7156 6 6.4343 6.8983 7.3938 7.9228 8.4872 22 The Solution (Table 5, n=3, i=10%) 3.6410 x 100 = 364.1 23 FV of Ordinary Annuity versus Annuity Due Ordinary Annuity 0 1 2 3 Annuity Due 0 DEP DEP DEP 1 2 3 DEP DEP DEP 24 8
Concluding Comments Part 5: Present Value of an Annuity Ordinary Annuity Annuity Due 25 9