At 5% per annual period for three periods, the growth factor is 1.157625 and
the discount factor is its reciprocal, approximately 0.8638376:
1.157625 × 0.8638376 ≈ 1
Multiplying a later amount by the discount factor moves it to the earlier
valuation date. Discounting does not mean subtracting rate × periods from the
future amount; that linear shortcut ignores compounding.
The operation does not choose its own rate. An accounting measurement needs the rate required by the applicable guidance and supported by the facts. A finance comparison needs a rate suited to the decision and cash-flow risk. Once that input is supplied, the arithmetic can translate dates; it cannot prove that the input was appropriate.
At a supplied positive rate, a positive single sum's earlier present value is below its later future value. At a zero rate they are equal. Those direction checks apply to this bounded deterministic model, not to every real-world cash- flow problem.
Round displayed currency only after the inverse check. Rounding a factor or intermediate amount at every step can create an artificial reconciliation difference, especially across many periods.
Put the concept to work
Understand this concept
- Explain discounting as multiplication by the reciprocal of the matching compound growth factor rather than as an unrelated subtraction of interest.
Apply this concept
- Apply a discount factor to a later single sum and reverse the result with the matching growth factor without premature rounding.
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Build on these ideas
- Compounding — Understand
To understand this concept: Helpful. The reciprocal relationship makes inverse checks visible.
- Discounting — Understand
To apply this concept: Required. Application must preserve the reciprocal relationship.
- Present value — Understand
To understand this concept: Required. Discounting is the operation that obtains a present value.
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Use this idea next
- Discounting — Apply
Required level here: understand. Required. Application must preserve the reciprocal relationship.
- Ordinary annuity — Apply
Required level here: apply. Helpful. Present value is the sum of discounted end-of-period payments.