Section PF.11 – Payout Annuities
In the last section you learned about annuities. In an annuity, you start with nothing, put money into an account on a regular basis, and end up with money in your account. In this section, we will learn about a variation called a Payout Annuity. With a payout annuity, you start with money in the account, and pull money out of the account on a regular basis. Any remaining money in the account earns interest. After a fixed amount of time, the account will end up empty. Payout annuities are typically used after retirement. Perhaps you have saved $500,000.00 for retirement, and want to take money out of the account each month to live on. You want the money to last you 20 years. This is a payout annuity.
| Payout Annuity Formula |
|
P0 = [latex]\large{\frac{PMT(1~-~(1~+~\frac{r}{n})^{-nt})}{\frac{r}{n}}}[/latex] P0 is the balance in the account at the beginning (starting amount, or principal). PMT is the regular withdrawal (the amount you take out each year, each month, etc.) r is the annual interest rate (APR) in decimal form (Example: 5% = 0.05) n is the number of compounding periods in one year. t is the number of years we plan to take withdrawals |
Like with annuities, the compounding frequency is not always explicitly given, but is determined by how often you take the withdrawals.
| When do you use the Payout Annuity Formula? |
|
Payout annuities assume that you take money from the account on a regular schedule (every month, year, quarter, etc.) and let the rest sit there earning interest. Compound interest: One deposit/starting balance Annuity: Repeated deposits. Payout Annuity: Repeated withdrawals |
| Example 1 |
| After retiring, you want to be able to take $1,000.00 every month for a total of 20 years from your retirement account. The account earns 6% interest. How much will you need in your account when you retire? |
|
Putting this into the equation: P0 = [latex]\large{\frac{1,000(1~-~(1~+~\frac{0.06}{12})^{-12~\cdot~20})}{(\frac{0.06}{12})}}[/latex] = $139,580.77 Using TVM Solver: N = 12*20 Once all of the given parameters are entered in, solve for PV. PV = -139,580.7717 You will need $139,580.78 in the account by the time you retire. |
| Example 2 |
| You know you will have $500,000.00 in your account when you retire. You want to be able to take annual withdrawals from the account for a total of 30 years. Your retirement account earns 8% interest. How much will you be able to withdraw each year? |
|
Putting this into the equation: 500,000 = [latex]\large{\frac{PMT(1~-~(1~+~\frac{0.08}{1})^{-1~\cdot~30})}{(\frac{0.08}{1})}}[/latex] Solve for PMT to get PMT = 44,413.71669 Using TVM Solver: N = 1*30 Once all of the given parameters are entered in, solve for PMT. PMT = 44,413.71669 So you would be able to withdraw $44,413.72 each year for 30 years. |
| You Try PF.11.A |
| After retiring, you want to be able to take $50,000.00 every year for a total of 25 years from your retirement account. The account earns 7% interest. How much will you need in your account when you retire? |
| Example 3 |
| You want to be able to withdraw $65,000.00 from your account each year for 30 years after you retire. You expect to retire in 25 years. If your account earns 6% interest, how much will you need to deposit each year until retirement to achieve your retirement goals? |
|
This problem requires two steps. Step 1: Initially, figure out how much money you need to have in your account at retirement so that you can withdraw $65,000.00 per year for 30 years. Step 2: After that, figure out how much money you need to deposit every year before retirement, so that you have the amount needed from Step 1 after 25 years. Step 1: Find the amount you need to have in your account at retirement so that you can make annual withdrawals of $65,000.00 per year for 30 years. N = 1*30 Once all of the given parameters are entered in, move your cursor to PV= and press ALPHA – ENTER. PV = $894,714.02. You need to have $894,714.02 in your retirement account so that you can withdraw $65,000.00 per year for 30 years. Step 2: Find the amount you need to deposit each year in order to have $894,714.02 in 25 years. N = 1*25 Once all of the given parameters are entered in, move your cursor to PMT= and press ALPHA – ENTER. PMT = -$16,307.70. You need to deposit $16,307.70 each year for 25 years, so that you will have enough money in your account when you retire to withdraw $65,000.00 per year for 30 years. |
Section PF.11 – Answers to You Try Problems
PF.11.A
You will need $582,679.16 in your account when you retire.
