How to Calculate Compound Interest With Fixed Annual Withdrawal


People save during their working years to have a steady income in their retirement years. One way to achieve this is to deposit money periodically in a savings account and let compounding grow your portfolio each year. Wealthy individuals often set up trust funds for family members and college scholarships for deserving students, which often rely on compound interest. The accumulated interest is the difference between the balance in a particular year and the initial deposit.

Get the principal amount of the deposit, annual interest rate and fixed annual withdrawal amounts. Your bank or investment manager should have this information.

Calculate the balance at the end of a certain number of years. The formula, in algebraic notation, is P x (1 + i)^n - (W x ((1 + i)^n - 1) / i). In this formula, "i" is the annual interest rate, "n" is the number of years, "P" is the original deposit amount and "W" is the fixed annual withdrawal.

For example, if you deposit $1 million, the interest rate is 8 percent compounding annually and the fixed annual withdrawal is $20,000, then the accumulated balance after 5 years is equal to about $1.353 million [$1 million x (1 + 0.08)^5 - (20,000 x ((1 + 0.08)^5 - 1) / 0.08) = $1 million x 1.08^5 - ($20,000 x (1.08^5 - 1) / 0.08) = $1.47 million - ($20,000 x 0.47 / 0.08) = $1.47 million - $117,332 = $1.353 million].

Subtract the balance at the end of a specified period from the original amount to get the compound interest. To conclude the example, the compound interest is equal to $1.353 million minus $1 million, or $353,000.

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