{"id":386,"date":"2016-10-12T16:24:30","date_gmt":"2016-10-12T16:24:30","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/math4libarts\/?post_type=chapter&#038;p=386"},"modified":"2019-05-30T16:55:16","modified_gmt":"2019-05-30T16:55:16","slug":"payout-annuities","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/chapter\/payout-annuities\/","title":{"raw":"Payout Annuities","rendered":"Payout Annuities"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Calculate the balance on an annuity after a specific amount of time<\/li>\r\n \t<li>Discern between compound interest, annuity, and payout annuity given a finance scenario<\/li>\r\n \t<li>Use the loan formula to calculate loan payments, loan balance, or interest accrued on a loan<\/li>\r\n \t<li>Determine which equation to use for a given scenario<\/li>\r\n \t<li>Solve a financial application for time<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Removing Money from Annuities<\/h2>\r\nIn 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.\r\n\r\nIn this section, we will learn about a variation called a <strong>Payout Annuity<\/strong>. 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.\r\n\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/12\/02204403\/2411468004_2bae893f5e_z.jpg\"><img class=\"aligncenter size-full wp-image-744\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/12\/02204403\/2411468004_2bae893f5e_z.jpg\" alt=\"Black and white aerial shot of hands exchanging money\" width=\"640\" height=\"426\" \/><\/a>\r\n\r\nPayout annuities are typically used after retirement. Perhaps you have saved $500,000 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. The formula is derived in a similar way as we did for savings annuities. The details are omitted here.\r\n<div class=\"textbox\">\r\n<h3>Payout Annuity Formula<\/h3>\r\n[latex]P_{0}=\\frac{d\\left(1-\\left(1+\\frac{r}{k}\\right)^{-Nk}\\right)}{\\left(\\frac{r}{k}\\right)}[\/latex]\r\n<ul>\r\n \t<li><em>P<sub>0<\/sub><\/em> is the balance in the account at the beginning (starting amount, or principal).<\/li>\r\n \t<li><em>d<\/em> is the regular withdrawal (the amount you take out each year, each month, etc.)<\/li>\r\n \t<li><em>r<\/em> is the annual interest rate (in decimal form. Example: 5% = 0.05)<\/li>\r\n \t<li><em>k<\/em> is the number of compounding periods in one year.<\/li>\r\n \t<li><em>N<\/em> is the number of years we plan to take withdrawals<\/li>\r\n<\/ul>\r\n<\/div>\r\nLike with annuities, the compounding frequency is not always explicitly given, but is determined by how often you take the withdrawals.\r\n<div class=\"textbox\">\r\n<h3>When do you use this?<\/h3>\r\nPayout 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.\r\n<ul>\r\n \t<li>Compound interest: One deposit<\/li>\r\n \t<li>Annuity: Many deposits.<\/li>\r\n \t<li>Payout Annuity: Many withdrawals<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nAfter retiring, you want to be able to take $1000 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?\r\n[reveal-answer q=\"261541\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"261541\"]\r\n\r\nIn this example,\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><em>d<\/em> = $1000<\/td>\r\n<td>the monthly withdrawal<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><em>r <\/em>= 0.06<\/td>\r\n<td>6% annual rate<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><em>k<\/em> = 12<\/td>\r\n<td>since we\u2019re doing monthly withdrawals, we\u2019ll compound monthly<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><em>N<\/em> = 20<\/td>\r\n<td>\u00a0since were taking withdrawals for 20 years<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nWe\u2019re looking for <em>P<sub>0:<\/sub><\/em>\u00a0how much money needs to be in the account at the beginning.\r\n\r\nPutting this into the equation:\r\n\r\n[latex]\\begin{align}&amp;{{P}_{0}}=\\frac{1000\\left(1-{{\\left(1+\\frac{0.06}{12}\\right)}^{-20(12)}}\\right)}{\\left(\\frac{0.06}{12}\\right)}\\\\&amp;{{P}_{0}}=\\frac{1000\\times\\left(1-{{\\left(1.005\\right)}^{-240}}\\right)}{\\left(0.005\\right)}\\\\&amp;{{P}_{0}}=\\frac{1000\\times\\left(1-0.302\\right)}{\\left(0.005\\right)}=\\$139,600 \\\\\\end{align}[\/latex]\r\n\r\nYou will need to have $139,600 in your account when you retire.\r\n\r\nNotice that you withdrew a total of $240,000 ($1000 a month for 240 months). The difference between what you pulled out and what you started with is the interest earned. In this case it is $240,000 - $139,600 = $100,400 in interest.\r\n\r\n[\/hidden-answer]\r\n\r\nView more about this problem in this video.\r\n\r\nhttps:\/\/youtu.be\/HK2eRFH6-0U\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n<iframe id=\"mom1\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=6687&amp;theme=oea&amp;iframe_resize_id=mom1\" width=\"100%\" height=\"300\"><\/iframe>\r\n\r\n&nbsp;\r\n\r\n<\/div>\r\n<div class=\"textbox\">\r\n<h3>Evaluating negative exponents on your calculator<\/h3>\r\nWith these problems, you need to raise numbers to negative powers.\u00a0 Most calculators have a separate button for negating a number that is different than the subtraction button.\u00a0 Some calculators label this (-) , some with +\/- .\u00a0 The button is often near the = key or the decimal point.\r\n\r\nIf your calculator displays operations on it (typically a calculator with multiline display), to calculate 1.005-240 you'd type something like:\u00a0 1.005 ^ (-) 240\r\n\r\nIf your calculator only shows one value at a time, then usually you hit the (-) key after a number to negate it, so you'd hit: 1.005 yx 240 (-) \u00a0=\r\n\r\nGive it a try - you should get 1.005-240 = 0.302096\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nYou know you will have $500,000 in your account when you retire. You want to be able to take monthly 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 month?\r\n[reveal-answer q=\"494776\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"494776\"]\r\n\r\nIn this example, we\u2019re looking for <em>d<\/em>.\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><em>r<\/em> = 0.08<\/td>\r\n<td>8% annual rate<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><em>k<\/em> = 12<\/td>\r\n<td>since we\u2019re withdrawing monthly<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><em>N<\/em> = 30<\/td>\r\n<td>30 years<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><em>P<sub>0<\/sub><\/em> = $500,000<\/td>\r\n<td>\u00a0we are beginning with $500,000<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nIn this case, we\u2019re going to have to set up the equation, and solve for <em>d<\/em>.\r\n\r\n[latex]\\begin{align}&amp;500,000=\\frac{d\\left(1-{{\\left(1+\\frac{0.08}{12}\\right)}^{-30(12)}}\\right)}{\\left(\\frac{0.08}{12}\\right)}\\\\&amp;500,000=\\frac{d\\left(1-{{\\left(1.00667\\right)}^{-360}}\\right)}{\\left(0.00667\\right)}\\\\&amp;500,000=d(136.232)\\\\&amp;d=\\frac{500,000}{136.232}=\\$3670.21 \\\\\\end{align}[\/latex]\r\n\r\nYou would be able to withdraw $3,670.21 each month for 30 years.\r\n\r\n[\/hidden-answer]\r\n\r\nA detailed walkthrough of this example can be viewed here.\r\n\r\nhttps:\/\/youtu.be\/XK7rA6pD4cI\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n<iframe id=\"mom2\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=6681&amp;theme=oea&amp;iframe_resize_id=mom2\" width=\"100%\" height=\"300\"><\/iframe>\r\n\r\n&nbsp;\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\nA donor gives $100,000 to a university, and specifies that it is to be used to give annual scholarships for the next 20 years. If the university can earn 4% interest, how much can they give in scholarships each year?\r\n[reveal-answer q=\"547109\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"547109\"]\r\n<div>\r\n\r\n<em>d<\/em> = unknown\r\n\r\n<em>r<\/em> = 0.04 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 4% annual rate\r\n\r\n<em>k<\/em> = 1\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 since we\u2019re doing annual scholarships\r\n\r\n<em>N<\/em> = 20 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 20 years\r\n\r\n<em>P0<\/em> = 100,000\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 we\u2019re starting with $100,000\r\n\r\n[latex]100,000=\\frac{d\\left(1-\\left(1+\\frac{0.04}{1}\\right)^{-20*1}\\right)}{\\frac{0.04}{1}}[\/latex]\r\n<div>\r\n\r\nSolving for <em>d<\/em> gives $7,358.18 each year that they can give in scholarships.\r\n\r\nIt is worth noting that usually donors instead specify that only interest is to be used for scholarship, which makes the original donation last indefinitely.\u00a0\u00a0 If this donor had specified that, $100,000(0.04) = $4,000 a year would have been available.\r\n\r\n<\/div>\r\n<\/div>\r\n[\/hidden-answer]\r\n\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Calculate the balance on an annuity after a specific amount of time<\/li>\n<li>Discern between compound interest, annuity, and payout annuity given a finance scenario<\/li>\n<li>Use the loan formula to calculate loan payments, loan balance, or interest accrued on a loan<\/li>\n<li>Determine which equation to use for a given scenario<\/li>\n<li>Solve a financial application for time<\/li>\n<\/ul>\n<\/div>\n<h2>Removing Money from Annuities<\/h2>\n<p>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.<\/p>\n<p>In this section, we will learn about a variation called a <strong>Payout Annuity<\/strong>. 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.<\/p>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/12\/02204403\/2411468004_2bae893f5e_z.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-744\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/12\/02204403\/2411468004_2bae893f5e_z.jpg\" alt=\"Black and white aerial shot of hands exchanging money\" width=\"640\" height=\"426\" \/><\/a><\/p>\n<p>Payout annuities are typically used after retirement. Perhaps you have saved $500,000 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. The formula is derived in a similar way as we did for savings annuities. The details are omitted here.<\/p>\n<div class=\"textbox\">\n<h3>Payout Annuity Formula<\/h3>\n<p>[latex]P_{0}=\\frac{d\\left(1-\\left(1+\\frac{r}{k}\\right)^{-Nk}\\right)}{\\left(\\frac{r}{k}\\right)}[\/latex]<\/p>\n<ul>\n<li><em>P<sub>0<\/sub><\/em> is the balance in the account at the beginning (starting amount, or principal).<\/li>\n<li><em>d<\/em> is the regular withdrawal (the amount you take out each year, each month, etc.)<\/li>\n<li><em>r<\/em> is the annual interest rate (in decimal form. Example: 5% = 0.05)<\/li>\n<li><em>k<\/em> is the number of compounding periods in one year.<\/li>\n<li><em>N<\/em> is the number of years we plan to take withdrawals<\/li>\n<\/ul>\n<\/div>\n<p>Like with annuities, the compounding frequency is not always explicitly given, but is determined by how often you take the withdrawals.<\/p>\n<div class=\"textbox\">\n<h3>When do you use this?<\/h3>\n<p>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.<\/p>\n<ul>\n<li>Compound interest: One deposit<\/li>\n<li>Annuity: Many deposits.<\/li>\n<li>Payout Annuity: Many withdrawals<\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>After retiring, you want to be able to take $1000 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?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q261541\">Show Solution<\/span><\/p>\n<div id=\"q261541\" class=\"hidden-answer\" style=\"display: none\">\n<p>In this example,<\/p>\n<table>\n<tbody>\n<tr>\n<td><em>d<\/em> = $1000<\/td>\n<td>the monthly withdrawal<\/td>\n<\/tr>\n<tr>\n<td><em>r <\/em>= 0.06<\/td>\n<td>6% annual rate<\/td>\n<\/tr>\n<tr>\n<td><em>k<\/em> = 12<\/td>\n<td>since we\u2019re doing monthly withdrawals, we\u2019ll compound monthly<\/td>\n<\/tr>\n<tr>\n<td><em>N<\/em> = 20<\/td>\n<td>\u00a0since were taking withdrawals for 20 years<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>We\u2019re looking for <em>P<sub>0:<\/sub><\/em>\u00a0how much money needs to be in the account at the beginning.<\/p>\n<p>Putting this into the equation:<\/p>\n<p>[latex]\\begin{align}&{{P}_{0}}=\\frac{1000\\left(1-{{\\left(1+\\frac{0.06}{12}\\right)}^{-20(12)}}\\right)}{\\left(\\frac{0.06}{12}\\right)}\\\\&{{P}_{0}}=\\frac{1000\\times\\left(1-{{\\left(1.005\\right)}^{-240}}\\right)}{\\left(0.005\\right)}\\\\&{{P}_{0}}=\\frac{1000\\times\\left(1-0.302\\right)}{\\left(0.005\\right)}=\\$139,600 \\\\\\end{align}[\/latex]<\/p>\n<p>You will need to have $139,600 in your account when you retire.<\/p>\n<p>Notice that you withdrew a total of $240,000 ($1000 a month for 240 months). The difference between what you pulled out and what you started with is the interest earned. In this case it is $240,000 &#8211; $139,600 = $100,400 in interest.<\/p>\n<\/div>\n<\/div>\n<p>View more about this problem in this video.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Payout Annuities\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/HK2eRFH6-0U?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"mom1\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=6687&amp;theme=oea&amp;iframe_resize_id=mom1\" width=\"100%\" height=\"300\"><\/iframe><\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<div class=\"textbox\">\n<h3>Evaluating negative exponents on your calculator<\/h3>\n<p>With these problems, you need to raise numbers to negative powers.\u00a0 Most calculators have a separate button for negating a number that is different than the subtraction button.\u00a0 Some calculators label this (-) , some with +\/- .\u00a0 The button is often near the = key or the decimal point.<\/p>\n<p>If your calculator displays operations on it (typically a calculator with multiline display), to calculate 1.005-240 you&#8217;d type something like:\u00a0 1.005 ^ (-) 240<\/p>\n<p>If your calculator only shows one value at a time, then usually you hit the (-) key after a number to negate it, so you&#8217;d hit: 1.005 yx 240 (-) \u00a0=<\/p>\n<p>Give it a try &#8211; you should get 1.005-240 = 0.302096<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>You know you will have $500,000 in your account when you retire. You want to be able to take monthly 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 month?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q494776\">Show Solution<\/span><\/p>\n<div id=\"q494776\" class=\"hidden-answer\" style=\"display: none\">\n<p>In this example, we\u2019re looking for <em>d<\/em>.<\/p>\n<table>\n<tbody>\n<tr>\n<td><em>r<\/em> = 0.08<\/td>\n<td>8% annual rate<\/td>\n<\/tr>\n<tr>\n<td><em>k<\/em> = 12<\/td>\n<td>since we\u2019re withdrawing monthly<\/td>\n<\/tr>\n<tr>\n<td><em>N<\/em> = 30<\/td>\n<td>30 years<\/td>\n<\/tr>\n<tr>\n<td><em>P<sub>0<\/sub><\/em> = $500,000<\/td>\n<td>\u00a0we are beginning with $500,000<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>In this case, we\u2019re going to have to set up the equation, and solve for <em>d<\/em>.<\/p>\n<p>[latex]\\begin{align}&500,000=\\frac{d\\left(1-{{\\left(1+\\frac{0.08}{12}\\right)}^{-30(12)}}\\right)}{\\left(\\frac{0.08}{12}\\right)}\\\\&500,000=\\frac{d\\left(1-{{\\left(1.00667\\right)}^{-360}}\\right)}{\\left(0.00667\\right)}\\\\&500,000=d(136.232)\\\\&d=\\frac{500,000}{136.232}=\\$3670.21 \\\\\\end{align}[\/latex]<\/p>\n<p>You would be able to withdraw $3,670.21 each month for 30 years.<\/p>\n<\/div>\n<\/div>\n<p>A detailed walkthrough of this example can be viewed here.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Payout annuity - solve for withdrawal\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/XK7rA6pD4cI?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"mom2\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=6681&amp;theme=oea&amp;iframe_resize_id=mom2\" width=\"100%\" height=\"300\"><\/iframe><\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p>A donor gives $100,000 to a university, and specifies that it is to be used to give annual scholarships for the next 20 years. If the university can earn 4% interest, how much can they give in scholarships each year?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q547109\">Show Solution<\/span><\/p>\n<div id=\"q547109\" class=\"hidden-answer\" style=\"display: none\">\n<div>\n<p><em>d<\/em> = unknown<\/p>\n<p><em>r<\/em> = 0.04 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 4% annual rate<\/p>\n<p><em>k<\/em> = 1\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 since we\u2019re doing annual scholarships<\/p>\n<p><em>N<\/em> = 20 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 20 years<\/p>\n<p><em>P0<\/em> = 100,000\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 we\u2019re starting with $100,000<\/p>\n<p>[latex]100,000=\\frac{d\\left(1-\\left(1+\\frac{0.04}{1}\\right)^{-20*1}\\right)}{\\frac{0.04}{1}}[\/latex]<\/p>\n<div>\n<p>Solving for <em>d<\/em> gives $7,358.18 each year that they can give in scholarships.<\/p>\n<p>It is worth noting that usually donors instead specify that only interest is to be used for scholarship, which makes the original donation last indefinitely.\u00a0\u00a0 If this donor had specified that, $100,000(0.04) = $4,000 a year would have been available.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-386\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Revision and Adaptation. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Payout Annuities. <strong>Authored by<\/strong>: David Lippman. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/www.opentextbookstore.com\/mathinsociety\/\">http:\/\/www.opentextbookstore.com\/mathinsociety\/<\/a>. <strong>Project<\/strong>: Ma. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>Payment. <strong>Authored by<\/strong>: Sergio Marchi. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/flic.kr\/p\/4F6pqy\">https:\/\/flic.kr\/p\/4F6pqy<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/\">CC BY-NC-ND: Attribution-NonCommercial-NoDerivatives <\/a><\/em><\/li><li>Payout Annuities. <strong>Authored by<\/strong>: OCLPhase2&#039;s channel. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/HK2eRFH6-0U\">https:\/\/youtu.be\/HK2eRFH6-0U<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li><strong>Authored by<\/strong>: OCLPhase2&#039;s channel. <strong>Provided by<\/strong>: Payout annuity - solve for withdrawal. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/XK7rA6pD4cI\">https:\/\/youtu.be\/XK7rA6pD4cI<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Question ID 6681, 6687. <strong>Authored by<\/strong>: Lippman,David. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: IMathAS Community License CC-BY + GPL<\/li><li>Payout Annuity Formula - Part 1, Part 2. <strong>Authored by<\/strong>: Sousa, James (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/zxRFWEj5v5w,%20https:\/\/youtu.be\/h3CWS9Rs7-s\">https:\/\/youtu.be\/zxRFWEj5v5w,%20https:\/\/youtu.be\/h3CWS9Rs7-s<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":20,"menu_order":7,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Payout Annuities\",\"author\":\"David Lippman\",\"organization\":\"\",\"url\":\"http:\/\/www.opentextbookstore.com\/mathinsociety\/\",\"project\":\"Ma\",\"license\":\"cc-by-sa\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Payment\",\"author\":\"Sergio Marchi\",\"organization\":\"\",\"url\":\"https:\/\/flic.kr\/p\/4F6pqy\",\"project\":\"\",\"license\":\"cc-by-nc-nd\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Payout Annuities\",\"author\":\"OCLPhase2\\'s channel\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/HK2eRFH6-0U\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"\",\"author\":\"OCLPhase2\\'s channel\",\"organization\":\"Payout annuity - 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