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Discounting with a negative periodic rate

With a negative periodic rate greater than −100%, the positive growth factor is below one, so dividing a fixed future payment by it can give a larger present value.

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Inspect the growth factor

For a rate of −0.5% per year, one year’s factor is 0.995. Over fifteen years it is 0.995¹⁵. A future payment of 1,000 has PV 1,000/0.995¹⁵, approximately 1,078.087. This is a mathematical learning example, not a market quotation.

Qualify the earlier-payment intuition

At a positive discount rate, receiving the same fixed amount earlier gives a larger present value. At a zero rate the timing does not change that amount’s PV. A negative rate reverses that comparison under the stated fixed-rate model.

Keep the factor within its defined domain

The regular discrete-period model here requires 1 + r to be positive. A rate of −100% creates a zero factor and cannot be used as an ordinary discount denominator.

Separate the rate model from other risks

The example does not establish that a promised payment is certain or that investing at a negative rate is appropriate for a particular person. Credit, liquidity, taxes and contractual terms remain separate questions.

Further references