Financial math: annuities, part I

Financial math awaits many students.  The tutor introduces annuities.

From the point of view of a typical consumer, an annuity is the reverse of a loan.  The consumer becomes the lender, while the institution pays them back, often with monthly payments.

Consider the following example:

Rhonda has personal resources of $185 000.  She buys an annuity that will pay her a fixed sum each month over the next 15 years.  What monthly payment can she expect if the interest rate being offered is 4.5% (compounded monthly)?

Solution:  For this question we’ll use the TI-83 Plus TVM solver (see my post here for how to use it:)

Set up the TVM solver by entering the following values:
PV=-185000 (negative because she’s paying it to the institution)
FV=0 (At the end, there’s nothing left.)
PMT:END (Found at bottom of screen; means each payment comes at month’s end.)

Now, go to PMT on the fourth line and press ALPHA ENTER.

Hopefully, you’ll receive the value 1415.24. 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.

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:)


Tan, S.T. Applied Finite Mathematics. Boston: Kent Publishing Company, 1990.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

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