**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 6^{th} 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 5^{th} year. And this value must account to,

This is in fact the annuity determining formula.

**Key terms**

**Solve now! Solutions**

**Problems**