{"id":7500,"date":"2022-03-28T12:52:25","date_gmt":"2022-03-28T07:22:25","guid":{"rendered":"https:\/\/www.goseeko.com\/blog\/?p=7500"},"modified":"2022-04-15T23:51:38","modified_gmt":"2022-04-15T18:21:38","slug":"what-is-annuity","status":"publish","type":"post","link":"https:\/\/www.goseeko.com\/blog\/what-is-annuity\/","title":{"rendered":"What is annuity?"},"content":{"rendered":"\n<p><strong>Annuity immediate- Present value and future value<\/strong><\/p>\n\n\n\n<p>An annuity is a sequence of equal payment or a sequence of regular payment at regular intervals or in other words. it is a fixed sum paid at regular intervals under certain conditions.<\/p>\n\n\n\n<p>The length of time during which the annuity is paid can either be until the death of the recipient or for a guaranteed minimum term of years, irrespective of whether the annuitant is alive or not.<\/p>\n\n\n\n<p>The time between payments is called the payment interval, and the time which the money is to be paid is called the term of the annuity.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Amount of an annuity<\/strong><\/h2>\n\n\n\n<p>Amount of an annuity is the total of all the installments left unpaid together with the compound interest of each payment for the period it remains unpaid.<\/p>\n\n\n\n<p>The formulas to find the amount of annuity are given below-<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/www.goseeko.com\/blog\/wp-content\/uploads\/2022\/03\/image-5.png?resize=464%2C150&#038;ssl=1\" alt=\"\" class=\"wp-image-7501\" width=\"464\" height=\"150\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Present value<\/strong><\/h2>\n\n\n\n<p>Present value of an annuity is the sum of the present values of all payments (or installments) made at successive annuity periods.<\/p>\n\n\n\n<p>The formulas to calculate present value \u2018V\u2019 of an annuity P are given below-<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/www.goseeko.com\/blog\/wp-content\/uploads\/2022\/03\/image-6.png?resize=482%2C145&#038;ssl=1\" alt=\"\" class=\"wp-image-7502\" width=\"482\" height=\"145\" \/><\/figure>\n\n\n\n<p><strong>The future value is calculated as-<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"256\" height=\"64\" src=\"https:\/\/i0.wp.com\/www.goseeko.com\/blog\/wp-content\/uploads\/2022\/03\/image-7.png?resize=256%2C64&#038;ssl=1\" alt=\"\" class=\"wp-image-7503\" \/><\/figure>\n\n\n\n<p><strong>Example: <\/strong><strong>Sundar decides to deposit 20,000rs. at the end of each year in a bank which pays 10% p.a. compound interest.<\/strong><\/p>\n\n\n\n<p><strong>If the installments are allowed to accumulate, what will be the total accumulation at the end of 9 years?<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Suppose A Rs. be the total accumulation at the end of 9 years. Then we get-<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"160\" height=\"50\" src=\"https:\/\/i0.wp.com\/www.goseeko.com\/blog\/wp-content\/uploads\/2022\/03\/image-8.png?resize=160%2C50&#038;ssl=1\" alt=\"\" class=\"wp-image-7504\" \/><\/figure>\n\n\n\n<p>Here P = 20,000 Rs., i = 10\/100 = 0.1 and n = 9<\/p>\n\n\n\n<p>Then<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"534\" height=\"76\" src=\"https:\/\/i0.wp.com\/www.goseeko.com\/blog\/wp-content\/uploads\/2022\/03\/image-9.png?resize=534%2C76&#038;ssl=1\" alt=\"\" class=\"wp-image-7505\" \/><\/figure>\n\n\n\n<p>Hence the total required accumulation is 2,71,590rs.<\/p>\n\n\n\n<p><strong>Example: Rajeev purchased a flat valued at 3,00,000rs. He paid 2,00,000rs. at the time of purchase and agreed to pay the balance with interest of 12% per annum compounded half yearly in 20 equal half yearly installments.<\/strong><\/p>\n\n\n\n<p><strong>If the first installment is paid after six months from the date of purchase, find the amount of each installment.<\/strong><\/p>\n\n\n\n<p><strong>[Given log 10.6 = 1.0253 and log 31.19 = 1.494]<\/strong><\/p>\n\n\n\n<p><strong>Solution<\/strong><\/p>\n\n\n\n<p>Here 2,00,000 has been paid at the time of purchase when cost of the flat was ` 3,00,000, we have to<\/p>\n\n\n\n<p>Consider 20 equated half yearly annuity payments Rs. P when 12% is rate of annual interest compounded half<\/p>\n\n\n\n<p>Yearly for present value of 1,00,000rs.<\/p>\n\n\n\n<p>So that-<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/www.goseeko.com\/blog\/wp-content\/uploads\/2022\/03\/image-10.png?resize=193%2C45&#038;ssl=1\" alt=\"\" class=\"wp-image-7506\" width=\"193\" height=\"45\" \/><\/figure>\n\n\n\n<p>or<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/www.goseeko.com\/blog\/wp-content\/uploads\/2022\/03\/image-11.png?resize=203%2C76&#038;ssl=1\" alt=\"\" class=\"wp-image-7507\" width=\"203\" height=\"76\" \/><\/figure>\n\n\n\n<p>then<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.goseeko.com\/369ccb0a-b850-45d7-ace8-f7ee438e965e\" alt=\"\" width=\"193\" height=\"61\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/www.goseeko.com\/blog\/wp-content\/uploads\/2022\/03\/image-13.png?resize=146%2C46&#038;ssl=1\" alt=\"\" class=\"wp-image-7509\" width=\"146\" height=\"46\" \/><\/figure>\n\n\n\n<p>Hence the amount of each installment&nbsp; = 8,718.40 Suppose,<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/www.goseeko.com\/blog\/wp-content\/uploads\/2022\/03\/image-14.png?resize=83%2C27&#038;ssl=1\" alt=\"\" class=\"wp-image-7510\" width=\"83\" height=\"27\" \/><\/figure>\n\n\n\n<p>Taking log-<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/www.goseeko.com\/blog\/wp-content\/uploads\/2022\/03\/image-15.png?resize=323%2C25&#038;ssl=1\" alt=\"\" class=\"wp-image-7511\" width=\"323\" height=\"25\" \/><\/figure>\n\n\n\n<p>Hence<\/p>\n\n\n\n<p>X = 0.3119<\/p>\n","protected":false},"excerpt":{"rendered":"<p>An annuity is a sequence of equal payment or a sequence of regular payment at regular intervals or in other words.<\/p>\n","protected":false},"author":28,"featured_media":4913,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[31],"tags":[],"class_list":["post-7500","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-maths"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.3.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>What is annuity? 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