Formula of perpetuity:
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,
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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