You just found out that you had a very eccentric uncle who lived quietly in Manhattan. He left you $35,000. You just saw the movie The Bucket List and have decided that you want to put some money away so that in 10 years, you can start fulfilling items on that list.
With whatever money you have left, you’ll pay off some bills. You have found an investment instrument that will pay 5% interest annually.
Use the scenarios along with the following factor table data to answer each of the questions. Note that the complete Future Value and Future Value Annuity tables (as well as the Present Value and Present Value Annuity tables) are located in the appendix in your text.
Factor Tables
Table of Present Value Factors
|
Interest Rate |
|||||
|---|---|---|---|---|---|
| Year | 3% | 5% | 7% | 8% | 9% |
| 6 | .837 | .746 | .666 | .630 | .596 |
| 8 | .789 | .677 | .582 | .540 | .502 |
| 10 | .744 | .614 | .508 | .463 | .422 |
| 12 | .701 | .557 | .444 | .397 | .356 |
| 15 | .642 | .481 | .362 | .315 | .275 |
| 20 | .554 | .377 | .258 | .215 | .178 |
Table of Present Value Annuity Factors
|
Interest Rate |
|||||
|---|---|---|---|---|---|
| Year | 3% | 5% | 7% | 8% | 9% |
| 6 | 5.417 | 5.076 | 4.767 | 4.623 | 4.486 |
| 8 | 7.020 | 6.463 | 5.971 | 5.747 | 5.535 |
| 10 | 8.530 | 7.722 | 7.024 | 6.710 | 6.418 |
| 12 | 9.954 | 8.863 | 7.943 | 7.536 | 7.161 |
| 15 | 11.938 | 10.380 | 9.108 | 8.560 | 8.061 |
| 20 | 14.878 | 12.462 | 10.594 | 9.818 | 9.129 |
Present Value of a Single Amount
What is the amount you should invest today to have $40,250 in 10 years?
Present Value of an Annuity
Now the 10 years have passed, and you are ready to pull some money out of your fund. You talked to your investment advisor who says you can take this money and move it into a fund that will earn 7% interest annually. And you envision tackling most of your bucket list items over the next 12 years.
What is the annual amount you will have to spend for your bucket list activities?
Answer 1:
Amount after 10 years = FV = $40,250
Rate of interest = 5%
Amount you should invest today = PV = FV * Present Value factor of $1 for 10 Years at discount rate of 5%
= 40250 * 0.614
= $24,713.50
Amount you should invest today = $24,713.50
Answer 2:
Amount at the end of 10 years = $40,250
Number of years = 12
Rate of interest = 7%
Annual amount you can draw at the end of each year = 40250 / Present value factor of $1 annuity for 12 years at 7%
= 40250 / 7.943
= $5067.35
Annual amount you can draw at the end of each year = $5,067.35
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