Example 23 - Time Required to Reach Goal

This example applies to our online demo Time Value of Money Calculator. The C-Value! program for Windows works in a similar way and has a few more features. Note, our online demo TVM calculator is limited to calculations using interest rates between 4.0% and 5.99%

Note:This topic has not been proofed and images need to be added. However, we believe that the steps are complete and accurate.

Calculating the time it takes to reach an investment goal.

1. Click the [New] button to clear any previous entries.
2. Set "Rounding" to "Ignore" by either:

• clicking on the "Rounding" button on the toolbar;
• clicking on the {Compute} menu choice and select {Rounding...};

1. This example is similar to example 14. Except that example 14 calculates the periodic amount required to reach a goal, this example illustrates the number of periodic cash flows required to reach a particular goal.
2. This example assumes that "Rounding" is initially set to "Last Withdrawal". (If the first event still says "Loan", then the option you should select will be "Last Payment".)
3. You desire to know how long it will take to save $49,100 assuming periodic deposits of $1,000 starting on January 3rd, 2005. The assumed nominal annual rate is 4.5% with "Daily" compounding.
4. 1) Open the C-Value! Setup Window. Press either [F6] or select {Settings}{Compute Setup} from the menu.
5. A) For the "Compute Method" select the "Normal" option.
6. B) Set the "Year Length" to 360.
7. C) Click on the [OK] button to close the Window.
8. 2) Set compounding to "Daily".
9. 3) Enter 4.500% for the "Nominal Annual Rate".
10. At this point we need to calculate when the balance will be equal to our goal of $49,100.00. To do this, we create a series of deposits with the "# Periods" set to a far greater number of periods than we need. Obviously, if we make a series of 100 deposits of $1,000 we'll far surpass our goal.
11. 4) Create the first event as a "Deposit".
12. A) Set the "Date" to January 3, 2005.
13. B) For the "Amount", enter $1,000
14. C) Enter 100 for the "# Periods".
15. D) Select "Monthly" for the "Frequency"
16. 5) Calculate the Date that the balance is equal to our goal.
17. A) Click on the menu {Compute} ->{Balance...} or press [Ctrl][B] to open the balance calculator.
18. B) Set the Date to "Unknown" by typing "U".
19. C) Set the Balance to our goal, $49,100.00.
20. D) Click the "Calculate" button. The result is 9/20/08.
21. E) Make a note of this date and click "Done" to close the window.
22. 6) On the first event row, set the "# Periods" to "Unknown".
23. 7) Create the 2nd event. It will be a "Withdrawal".
24. A) Enter the "Date" as September 20, 2008 from 5D above.
25. B) Enter the "Amount" as $49,100 which is our goal.
26. C) Enter 1 for "# Periods"
27. 8) Click calculate. The number of periodic deposits that will be required is 45. Furthermore, you'll need to wait an additional 17 days from the final deposit to accrue enough interest to reach your goal. The actual withdrawal amount will be $49,097.74.
28. NOTE: The difference between the actual withdrawal of $49,097.74 and the desired amount, $49,100.00 is $2.26, or less than one day's interest.
29. FURTHER NOTE: Sometimes the "error" amount will be much greater and it will appear that C-Value! maybe is not calculating a correct balance date. Most likely, this is not the case. The goal amount in the example was carefully selected to illustrate this point. Rather than have a goal of $49,100. Try the same example but set a goal of $49,500. If you do this, you'll see that the resulting date in step 5D) above will be 10/03/2008. The calculated periods will be 45, but the final withdrawal amount will be $49,177.58. Which is over $300 shy of our goal.
30. Why's this, you ask. Simple, if we were to add just one more day to the result of the calculated date, then the total periods calculated would have been 46 (and not 45) and another $1,000 deposit would have been added to the cash flow and the difference between the withdrawal on Oct 4th and the desired goal would have been even greater than $300.00.
31. Of course, with C-Value!'s flexibility, you could set a withdrawal date of Oct. 4th or even the 5th, not have a deposit on Oct 3rd and you're final withdrawal will be very close to your goal amount.

Back to the online Time Value of Money Calculator.