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Formula of perpetuity:

Perpetuity and Annuity Derivations 59When you wish to prove on an account of this being a real statement, the divide it by C,

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Multiplying the 3.5 equation by the factor which is (1 + r),

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Subtracting the equation 3.5 from that of the equation given in 3.6,

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This right hand side simplifies directly into the r/r that makes it a real statement.

Growing perpetuity on the other hand gives us a formula,

Perpetuity and Annuity Derivations 63Returning to the original definition, a perpetuity (growing) will pull out a (1 + g) of the factor who is from the cash flows,

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The f is replaced by Perpetuity and Annuity Derivations 65 using the very first of the formula,

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This can be further simplified into,

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Annuity is considered as a perpetuity value which will pay a fixed amount of $10 always in the starting of the first year.

Another thing that must be considered is that the perpetuity begins in the five years & pays $10 that is beginning at the 6th year. If you are to purchase a total of $10 every year for the duration of 5 years, then that would be so for $0 every year after that year.

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This will show that $10 is the beginning of the next coming year and in the ending of the 5th year. And this value must account to,

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This is in fact the annuity determining formula.

Key terms

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Solve now! Solutions

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Problems

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