# The tutor continues exploring annuities.

In my previous post I introduced the idea of an annuity with an example. That example had each payment at month’s-end; hence, it was an **ordinary annuity**.

With an **annuity due**, the payment is received at the beginning of the month.

Using, once again, the TI-83 Plus TVM solver, we’ll rework yesterday’s example as if it is an annuity due; i.e., each payment comes at month’s beginning:

Recall that the annuity was purchased for $185 000, offered interest of 4.5% (compounded monthly), and was to be paid monthly over 15 years. We’ll set up the TI-83 Plus TVM solver (see my post here for how to use it) with the following parameters:

N=15×12

I%=4.5

PV=-185000 (negative because it’s being paid out)

PMT:*leave this one blank for now*

FV=0 (at the end of the 15 years, there’s nothing left)

P/Y=12 (12 payments per year)

C/Y=12 (monthly compounding periods)

PMT:BEGIN (Payment at beginning of month: annuity due)

The PMT entry on the fourth line we leave blank at first; for the one at the bottom, we choose BEGIN.

After all the parameters are entered, we return to the PMT on the fourth line and key in ALPHA ENTER. Hopefully, the value 1409.95 appears.

Notice that, when this was an ordinary annuity (once again, see yesterday’s post), the payment was $1415.24.

There is still more to say about annuities, and of course how to find their payments on other makes of financial calculator. I’ll be offering more coverage in future posts:)

Source:

Tan, S.T. *Applied Finite Mathematics*. Boston: PWS-KENT Publishing Company, 1990.

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