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Suppose we were given a discounted cost of $50,000, which has been generated using a discount factor of 3.5% and a time-horizon of 45 years.

Is it possible to obtain what the non-discounted cost is today?

For clarity, this is not as part of a test. Instead, it is an intellectual curiosity, where I simplified the figures taken from Page 4, Paragraph 4 of this paper:

https://www.england.nhs.uk/wp-content/uploads/2018/07/patent-foramen-ovale-closure-evaluation-report.pdf

My own intuition would be that the sign of the exponent is flipped, would this be correct?

Feedback from the mathematicians would be appreciated,

Best,

Andrew

saulspatz
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EB3112
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  • This is not about sequences and series. That relates to infinite sequences and series. The question just relates to compound interest. I've changed the tag to actuarial science, in which compound interest is a matter of concern. – saulspatz Sep 06 '19 at 14:25
  • It isn't clear to me what is meant by "the non-discounted cost today." Are you asking for the total non-discounted costs? That is, the sum of future cash flows, without regard to the effects of interest or inflation? If so, you don't "just flip the exponents," you simply don't discount. – saulspatz Sep 06 '19 at 14:32
  • No, precisely Saulspatz. I understand the concept of discounting. However, if you're presented with the discounted figure, is it possible to reveal what would be the non-discounted figure? I.e. not discounted 45 times, at 0.035% – EB3112 Sep 06 '19 at 18:59
  • No, it isn't. Near-term cash flows are weighted heavier than long-term cash flows, so you can replace an immediate outlay of $$100$ by an outlay of $$100\cdot(1.035)^{10}$ ten years from now and get the same discounted value. Of course, the sum of the cash flows will be different. – saulspatz Sep 06 '19 at 19:05
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    Hi Saul, thanks for your feedback. Sincerely. I appreciate your engagement with the question. However, in this instance, this is nothing to do with cash flows. Instead, there is a nominal cost today, but because the person is having their health invested in (and the typical investment benefit will last 45 years), then discounting is carried out on costs and benefits in this circumstance. The one off cost is discounted because it forms cost effectiveness expression (along with benefits), and in the absence of discounting both - the cost-effectiveness expression would be misleading. – EB3112 Sep 06 '19 at 19:17
  • Costs and benefits are measured in money though, so we have nominal cash flows. Even if they're measured in some other units, they're just numbers, and my comment is strictly arithmetical. – saulspatz Sep 06 '19 at 19:24

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