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# Example 22 - Rate of Return on an Annuity

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 2.0% and 8.9%

## Calculating the rate of return on an annuity.

For greater detail about how values are entered into the TVM calculator, please see Example 1 - conventional mortgage or loan.

Background: When evaluating an annuity (or any investment) one will usually want to know the rate of return (commonly called "ROI" for "return on investment"). Generally, the annuity with the higher rate of return, assuming everything else being equal, is preferable over one with the lower rate of return. This example will show you how to evaluate one annuity. The point, of course, is to use this technique to evaluate two or more annuities and compare the results. You can use this calculation to answer such questions as "is annuity "A" generating a higher rate of return with a single payment amount or annuity "B" with a higher initial payment amount and a lower payment amount paid to the survivor?"

This example assumes that the annuity has an up front cost of \$1,500,000. That there will be a monthly withdrawal of \$8,775 for 20 years and then the withdrawal will be reduced to 65% of the initial withdrawal amount (due to the death of one spouse) and payable for another 10 years.

To calculate the rate of return, follow these steps:

1. Click the [New] button to clear any previous entries.
2. Set "Rounding" to "Ignore" by clicking on the "Rounding" button.
1. Click {Setup} select {Set calculation options...} from the top menu.
1. For the "Compute/Amortization Methods" select "Normal"
2. Set the "Days Per Year" to 360.
3. Click on the [OK] button to close the Window.
1. Set compounding to "Daily".
2. Enter "Unknown" for the "Nominal Annual Rate".
3. Create the first event as a "Deposit". We use the Deposit event here because we are assuming you will be buying the annuity and thus depositing funds for future withdrawal. See event names and creating event names using the events setup dialog window for more details.
1. Set the "Date" to November 1, 2012. (mm/dd/yyyy)
2. For the "Amount", enter \$1,500,000.00. (This is the cost of the annuity, or the amount invested.)
3. Enter 1 for the "# Periods".
1. Create the 2nd event. It will be a "Withdrawal".
1. Enter the "Date" as December 1, 2012
2. Enter the "Amount" as \$8,775.
3. Enter 240 for "# Periods" (20 years of monthly withdrawals)
4. Select "Monthly" for "Frequency". Then "End Date" will be November 1, 2032. That is, the last withdrawal for this series will be on this date.
1. Create the 3rd event. It will also be a "Withdrawal". (Here's where we assume the withdrawal will be reduced.)
1. Enter the "Date" as December 1, 2032
2. Enter the "Amount" as \$5,703.75.
3. Enter 120 for "# Periods" (10 years of monthly withdrawals)
4. Select "Monthly" for "Frequency". Then "End Date" will be November 1, 2042.
5. The calculator will now look like this:

1. Click on [Calc] button. The "Annual Rate" is 5.093%. (You may have to give this calculation a couple of seconds — it is solved by iteration.)
1. Click on the [>>] button to the right of the Annual Rate. The effective rate is 5.225% is considered by many to be the annualized rate of return This value is the result that Excel calculates as the XIRR.

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