Lesson Find future value of an Ordinary Annuity saving plan
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<H2>Find future value of an Ordinary Annuity saving plan</H2> <H3>Problem 1</H3>You deposit $5000 at the end of each year into an account, earning 4% interest compounded annually. How much will you have in the account in 20 years? <B>Solution</B> <pre> It is a classic Ordinary Annuity saving plan. The general formula is FV = {{{P*(((1+r)^n-1)/r)}}}, (1) where FV is the future value of the account; P is the annual payment (deposit); r is the annual percentage rate presented as a decimal; n is the number of deposits (= the number of years, in this case). Under the given conditions, P = 5000; r = 0.04; n = 20. So, according to the formula (1), you get at the end of the 20-th year FV = {{{5000*(((1+0.04)^20-1)/0.04)}}} = $148890.39. Note that you deposit only 20*$5000 = $100,000. The rest is what the account earns/accumulates in 20 years. </pre> <H3>Problem 2</H3>Eric deposits $900 at the end of each quarter to his saving account which is compounded quarterly at 4% annual percent yield. What is the accumulated total in Eric's account at the end of 20-th year ? <B>Solution</B> <pre> It is a classic Ordinary Annuity saving plan. The general formula is FV = {{{P*(((1+r)^n-1)/r)}}}, (1) where FV is the future value of the account; P is your quarterly payment (deposit); r is the quarterly percentage yield presented as a decimal; n is the number of deposits (= the number of years multiplied by 4, in this case). Under the given conditions, P = 900; r = 0.04/4; n = 4*20 = 80. So, according to the formula (1), Eric will get at the end of the 20-th year FV = {{{900*(((1+0.04/4)^(4*20)-1)/((0.04/4)))}}} = {{{900*((1.01^80-1)/0.01)}}} = $109,504.37. Note that Eric deposits only 4*20*$900 = $72,000. The rest is what the account earns/accumulates in 20 years. </pre> <H3>Problem 3</H3>Bill deposits $300 at the end of each month to his saving account which is compounded monthly at 4% annual percent yield. What is the accumulated total in Bill's's account at the end of 20-th year ? <B>Solution</B> <pre> It is a classic Ordinary Annuity saving plan. The general formula is FV = {{{P*(((1+r)^n-1)/r)}}}, (1) where FV is the future value of the account; P is your monthly payment (deposit); r is the monthly percentage yield presented as a decimal; n is the number of deposits (= the number of years multiplied by 12, in this case). Under the given conditions, P = 300; r = 0.04/12; n = 12*20 = 240. So, according to the formula (1), you get at the end of the 20-th year FV = {{{300*(((1+0.04/12)^(12*20)-1)/((0.04/12)))}}} = {{{300*(((1+0.04/12)^240-1)/((0.04/12)))}}} = $110,032.39. Note that Bill deposits only 12*20*$300 = $72,000. The rest is what the account earns/accumulates in 20 years. </pre> \\\\\\\\\\\\\\\\\\\\\\\\ To make such complicated calculations as they are in this problem, you should have/use an appropriate calculator for such long formulas. Ideal choice is MS Excel, if you have it in your computer. Then you write a formula in a text editor, copy-paste it into an Excel work-sheet cell and click "Enter" - the result is ready in the next second. If you have no MS Excel in your computer, you may find similar free of charge calculators in the Internet. One such calculator is www.desmos.com/calculator It allows you to do the same thing: you write a formula in a text editor, copy-paste it into this calculator and click "Enter" - the result is ready in the next instance. //////////////////////// On Ordinary Annuity saving plans, see the lessons - <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Ordinary-Annuity-saving-plans-and-geometric-progressions.lesson>Ordinary Annuity saving plans and geometric progressions</A> - <A HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Solved-problem-on-Ordinary-Annuity-saving-plans.lesson>Solved problems on Ordinary Annuity saving plans</A> in this site. These lessons contain EVERYTHING you need to know about this subject, in clear and compact form. When you learn from these lessons, you will be able to solve similar problems and to perform similar calculations in semi-automatic mode. 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