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The present value of an annuity falls when interest rates rise

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That is true, if you raise the rate then the present value falls.Of course, the present value will fall assuming the existence of positive cash flows. This annuity present value is divided into four pieces which are: the present value (PV), the periodic cash flow (C), the discount rate (r), and the number of payments, or the life of the annuity, (T).
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