From the point of view of a typical consumer, an annuity is the reverse of a loan.\u00a0 The consumer becomes the lender, while the institution pays them back, often with monthly payments.<\/p>\n
Consider the following example:<\/p>\n
Rhonda has personal resources of $185 000.\u00a0 She buys an annuity that will pay her a fixed sum each month over the next 15 years.\u00a0 What monthly payment can she expect if the interest rate being offered is 4.5% (compounded monthly)?<\/p>\n
Solution:\u00a0 For this question we’ll use the TI-83 Plus TVM solver (see my post here<\/a> for how to use it:)<\/p>\n Set up the TVM solver by entering the following values: Now, go to PMT on the fourth line<\/strong> and press ALPHA<\/span> ENTER<\/span>.<\/p>\n Hopefully, you’ll receive the value 1415.24<\/span>. This value is positive because she will receive it. Apparently, Rhonda can anticipate receipt of $1415.24 per month for the next 15 years if she purchases the annuity described above.<\/p>\n Of course, the institution that sells the annuity must hope that by investing Rhonda’s money, they can do better than the 4.5% they are offering her. Why they might believe this, and some ideas about how they might do so, I’ll discuss in future posts:)<\/p>\n Source:<\/p>\n Tan, S.T. Applied Finite Mathematics<\/em>. Boston: Kent Publishing Company, 1990.<\/p>\n
\nN=15×12
\nI%=4.5
\nPV=-185000 (negative because she’s paying it to the institution)
\nFV=0 (At the end, there’s nothing left.)
\nP\/Y=12
\nC\/Y=12
\nPMT:END (Found at bottom of screen; means each payment comes at month’s end.)<\/p>\n