Quick questions on Annuities and future value: deriving the formula and applying it to regular savings

2short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is watching the future value build up, stage by stage?

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To see why this is a sum and not a single power, build the future value one deposit at a time. Take four annual deposits of $2000 into an account paying

6\%

per annum, valued just after the fourth deposit. Each deposit is drawn as a bar showing what it is worth at the end: the earliest deposit has compounded longest, so it is the tallest, and the running total appears under each panel.

What is wrong direction in the rearranged formula?

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When solving for

M

, the formula is

M = \frac{A r}{(1 + r)^n - 1}

, not

M = \frac{A}{(1 + r)^n}

(that is a single lump-sum discount).

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