Annuity Timelines and Payment Timing

≈ 25 min

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Annuity Timelines and Payment Timing

Ordinary annuity payments occur at period ends; annuity-due payments occur at beginnings and therefore earn one extra period of growth. A timeline prevents off-by-one errors in $n$ and in the focal date.

Worked reasoning

Every annuity-due payment earns one extra period.
Multiply the ordinary-annuity value by $1+i=1.02$ .
$50000(1.02)=51000$ .

Key idea

Payment timing determines the number of growth or discount intervals.

An ordinary annuity has future value R50 000. At the same rate, what is the annuity-due value if the periodic rate is 2%?

Which statement best captures the central mathematical idea in Annuity Timelines and Payment Timing?

Payment timing determines the number of growth or discount intervals.

Beginning- and end-of-period annuities have equal values at the same date.

A memorised formula is valid even when its conditions are not met.

The diagram or notation replaces the need to justify each mathematical step.

When starting a problem about Annuity Timelines and Payment Timing, which move is most reliable?

Draw payment dates and mark the focal date before selecting a formula.

Round every value before identifying the mathematical structure.

Choose the longest available formula and substitute immediately.

Assume the desired conclusion and work backwards without checking equivalence.

Which statement is a misconception that must be rejected when working with Annuity Timelines and Payment Timing?

Beginning- and end-of-period annuities have equal values at the same date.

Payment timing determines the number of growth or discount intervals.

Draw payment dates and mark the focal date before selecting a formula.

Count arrows between each payment and the focal date.

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