Quick questions on Annuities and Perpetuities - TCE Mathematics Applications (Tasmania)

The balance of an annuity behaves exactly like a loan balance: interest is added, then the payment is withdrawn.

A perpetuity pays forever because each payment is set exactly equal to the interest earned. The principal is never touched, so the balance stays constant period after period.

For long drawdowns it is impractical to iterate by hand, so TASC expects the finance (TVM) solver. Enter the present value as the lump sum invested, the per-period interest rate, the regular payment as the withdrawal, and solve for the unknown, usually the number of periods $n$ or the payment that empties the fund in a set time. The sign convention matters: the lump sum invested is entered as a negative present value (money paid in) and the withdrawal as a positive payment (money received), or consistently the other way round. Getting the signs consistent is what makes the solver return a sensible answer rather than an error.