HSC · Mathematics Advanced · Financial mathematics · also VCE Recursion & Financial Modelling live from the app

Annuities and Perpetuities

An annuity pays out from an invested lump sum until it's exhausted; a perpetuity pays forever because you only ever draw the interest. Same machinery as a loan, run in the other direction. This is the real knowscape from knowhere, not a picture of one. Drag it. Watch what actually changes.

mathematics advanced · financial mathematics · annuities and perpetuitiesdrag it · it is yours
the one idea

why this one carries the topic.

A loan and an annuity are the same machine facing opposite directions. Each period the balance is multiplied by (1 + r), and then a payment moves it — down for a loan, up for an investment. Every formula in this topic is that one step repeated, which is why the future value of an annuity turns out to be nothing more exotic than the sum of a geometric series.

An annuity depletes a lump sum by making regular withdrawals that exceed the interest earned, while a perpetuity only withdraws the interest so the principal remains intact forever.

what examiners catch — Examiners test whether students can identify that a perpetuity requires the withdrawal amount to exactly equal the interest earned each period, not exceed it.
what you leave with

four things, not forty.

what's underneath

nothing here is a standalone fact.

knowhere maps every concept to what it rests on and what rests on it — 2 underneath this one, 0 built on top. Each one says why, in a sentence, not as an arrow on a diagram.

this conceptannuities and perpetuitiesAn annuity depletes a lump sum by making regular withdrawals that exceed the interest earned, while a perpetuity only withdraws the interest so the principal remains intact forever.
sits under itgeometric growth and compound interestbecause an annuity is the loan run in reverse
sits under itreducing balance loansbecause same recurrence, opposite direction
the rest of financial mathematics

3 more, same treatment.

Each one is its own knowscape in the app — built for how a particular student takes things in, not one explanation handed to everybody.

annuities and investment growthin the appreducing balance loansin the appfuture value of annuitiesin the app
this is one of 865

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knowherehsc mathematics advancedannuities and perpetuities