Perpetuity and Annuity Derivations

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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,

Perpetuity and Annuity Derivations 60

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

Perpetuity and Annuity Derivations 61

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

Perpetuity and Annuity Derivations 62

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,

Perpetuity and Annuity Derivations 64

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

Perpetuity and Annuity Derivations 66

This can be further simplified into,

Perpetuity and Annuity Derivations 67

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,

Perpetuity and Annuity Derivations 69

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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