Formula of perpetuity: When you wish to prove on an account of this being a real statement, the divide it by C, Multiplying the 3.5 equation by the factor which is (1 + r), Subtracting the equation 3.5 from that of the equation given in 3.6, 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, Returning to the original definition, a perpetuity (growing) will pull out a (1 + g) of the factor who is from the cash flows, The f is replaced by using the very first of the formula, This can be further simplified into, 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. 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, This is in fact the annuity determining formula.

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