{"id":3376,"date":"2021-06-29T11:14:29","date_gmt":"2021-06-29T15:14:29","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/?post_type=chapter&#038;p=3376"},"modified":"2021-06-29T19:00:39","modified_gmt":"2021-06-29T23:00:39","slug":"videos-back-to-back-annuities","status":"web-only","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/chapter\/videos-back-to-back-annuities\/","title":{"raw":"Videos: Back-to-Back Annuities","rendered":"Videos: Back-to-Back Annuities"},"content":{"raw":"<h2><em>Deferred Annuities<\/em><\/h2>\r\n1. You plan to retire in 21 years.\u00a0 You will need 25 annual payments of $30,000 with the first payment to be received in 21 years.\u00a0 Interest is calculated at 10% effective.\r\n\r\n(a)\u00a0\u00a0 How much money should you set aside today for your retirement?\r\n\r\n[embed]https:\/\/youtu.be\/C0MaQi9fLeI[\/embed]\r\n<h2>Back-to-Back Annuities<\/h2>\r\n(b)\u00a0\u00a0 Instead of making one large payment you would like to make 21 annual payments starting today.\u00a0 Find the size of these payments.\r\n\r\n[embed]https:\/\/youtu.be\/85g5NEA-Xu4[\/embed]\r\n\r\n(c)\u00a0\u00a0 How much of your retirement annuity in part (b) is interest?\r\n\r\n(d)\u00a0\u00a0 Re-answer b, assuming you make the payments starting in one year.\r\n\r\n(e)\u00a0\u00a0 How much of your retirement annuity in part (d) is interest?\r\n\r\n[embed]https:\/\/youtu.be\/BTJu2ckkY3w[\/embed]\r\n\r\n&nbsp;\r\n\r\n2. You are saving money for your retirement.\u00a0 Starting in six months and for five years you invest $1,500 every 6 months in a mutual fund that pays 6% compounded semi-annually. After five years, the rate drops to 4.8% compounded quarterly and you decide to deposit $1,000 every quarter for another five years.\u00a0 How much money will you have at the end of ten years?\r\n\r\n[embed]https:\/\/youtu.be\/nH3VbWbnzNo[\/embed]\r\n\r\n&nbsp;\r\n\r\n3.\u00a0 You would like to save enough to take a 2 year sabbatical in 15 years.\u00a0 Starting today, you make your first of 180 monthly deposits of $500 into an account that pays <em>j<sub>12<\/sub><\/em>=9%.\r\n\r\n(a)\u00a0\u00a0 One month after making your last deposit you take your first of 24 monthly payments.\u00a0 Find the size of these payments.\r\n\r\n(b)\u00a0\u00a0 Two months after making your last deposit you take your first of 24 monthly payments.\u00a0 Find the size of these payments.\r\n\r\n[embed]https:\/\/youtu.be\/37iJXaf-rRA[\/embed]\r\n<h2>Summary of Back to Back Annuities<\/h2>\r\n[embed]https:\/\/youtu.be\/Mn5nQyKlkFQ[\/embed]","rendered":"<h2><em>Deferred Annuities<\/em><\/h2>\n<p>1. You plan to retire in 21 years.\u00a0 You will need 25 annual payments of $30,000 with the first payment to be received in 21 years.\u00a0 Interest is calculated at 10% effective.<\/p>\n<p>(a)\u00a0\u00a0 How much money should you set aside today for your retirement?<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Business Math Lesson 14: Back-to-back Annuities, part 1\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/C0MaQi9fLeI?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2>Back-to-Back Annuities<\/h2>\n<p>(b)\u00a0\u00a0 Instead of making one large payment you would like to make 21 annual payments starting today.\u00a0 Find the size of these payments.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Business Math Lesson 14: Back-to-back Annuities, part 2\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/85g5NEA-Xu4?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>(c)\u00a0\u00a0 How much of your retirement annuity in part (b) is interest?<\/p>\n<p>(d)\u00a0\u00a0 Re-answer b, assuming you make the payments starting in one year.<\/p>\n<p>(e)\u00a0\u00a0 How much of your retirement annuity in part (d) is interest?<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-3\" title=\"Business Math Lesson 14: Back-to-back Annuities, part 3\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/BTJu2ckkY3w?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>&nbsp;<\/p>\n<p>2. You are saving money for your retirement.\u00a0 Starting in six months and for five years you invest $1,500 every 6 months in a mutual fund that pays 6% compounded semi-annually. After five years, the rate drops to 4.8% compounded quarterly and you decide to deposit $1,000 every quarter for another five years.\u00a0 How much money will you have at the end of ten years?<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-4\" title=\"Business Math Lesson 14: Back-to-back Annuities, part 4\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/nH3VbWbnzNo?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>&nbsp;<\/p>\n<p>3.\u00a0 You would like to save enough to take a 2 year sabbatical in 15 years.\u00a0 Starting today, you make your first of 180 monthly deposits of $500 into an account that pays <em>j<sub>12<\/sub><\/em>=9%.<\/p>\n<p>(a)\u00a0\u00a0 One month after making your last deposit you take your first of 24 monthly payments.\u00a0 Find the size of these payments.<\/p>\n<p>(b)\u00a0\u00a0 Two months after making your last deposit you take your first of 24 monthly payments.\u00a0 Find the size of these payments.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-5\" title=\"Business Math Lesson 14: Back-to-back Annuities, part 5\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/37iJXaf-rRA?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2>Summary of Back to Back Annuities<\/h2>\n<p><iframe loading=\"lazy\" id=\"oembed-6\" title=\"Business Math Lesson 14: Back-to-back Annuities, part 6\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/Mn5nQyKlkFQ?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n","protected":false},"author":883,"menu_order":18,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-3376","chapter","type-chapter","status-web-only","hentry"],"part":46,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapters\/3376","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/users\/883"}],"version-history":[{"count":1,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapters\/3376\/revisions"}],"predecessor-version":[{"id":3377,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapters\/3376\/revisions\/3377"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/parts\/46"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapters\/3376\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/media?parent=3376"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapter-type?post=3376"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/contributor?post=3376"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/license?post=3376"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}