How to Calculate Growing Annuity
- 1). Determine the initial cash flow, the applicable interest rate, the growth rate of the annuity and the number of periods of the annuity. For example, an investor may receive $200, and that will grow 5 percent with each yearly payment. The current interest rate is 8 percent. The annuity disburses over five years.
- 2). Subtract the interest rate from the growth rate. Then divide one by the difference. In our example, 8 percent minus 5 percent equals 3 percent, then 1 / 0.03 equals 33.33.
1/(r-g)) - 3). Add 1 to the growth rate. In our example, 1 plus 0.05 equals 1.05.
1+g - 4). Add 1 to the interest rate. In our example, 1 plus 0.08 equals 1.08.
1+r)) - 5). Divide the number calculated in Step 3 by the number calculated in Step 4. In our example, 1.05 divided by 1.08 equals 0.9722.
- 6). Raise the number calculated in Step 5 by the number of periods for the annuity. In our example, 0.9722 raised to the power of 5 equals 0.868616.
- 7). Multiply the number calculated in Step 2 by the number calculated in Step 6. In our example, 33.33 times 0.868616 equals 28.95386.
- 8). Subtract the number calculated in Step 7 from the number calculated in Step 2. In our example, 33.33 minus 28.95386 equals 4.379474.
- 9). Multiply the initial deposit by the number calculated in Step 8. In our example, $200 times 4.379474 equals $875.90.
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