# Annuity - Essay 2

-consists of a series of equal payments made at equal intervals of time

- are primarily used as a means of securing a steady cash flow for an individual during their retirement years

- can be structured according to a wide array of details and factors, such as the duration of time that payments from the annuity can be guaranteed to continue. Annuities can be created so that, upon annuitization, payments will continue so long as either the annuitant or their spouse is alive. Alternatively, annuities can be structured to pay out funds for a fixed amount of time, such as 20 years, regardless of how long the annuitant lives.

Annuities occur in following instances:

* Payment of a debt by a series of equal payments at equal intervals of time. * Accumulation of a certain amount by setting equal amounts periodically. * Substitution of a series of equal amounts periodically in lieu of a lump sum at retirement of an individual.

Types of Annuities:

* Ordinary Annuity

-is one where the equal payments are made at the end of each payment period starting from the first period. * Deferred Annuity

-is one where the payment of the first amount is deferred a certain number of periods after the first. * Annuity Due

-is one where the payments are made at the start of each period, beginning from the first period. * Perpetuity

-is an annuity where the payment periods extend forever or in which the periodic payments continue indefinitely.

Capitalized Cost (an application of perpetuity)

-The capitalized cost of any structure or property (equipment, machinery, building, etc.) is the sum of its cost and the present worth of all costs for replacement, operation, and maintenance for a long time or forever.

Capitalized Cost= First Cost + Cost of Perpetual Maintenance

To derive the formula;

Let:

FC= first cost of the structure

S= the amount needed to replace or maintain the property every k periods

X= the amount of principal invested at i% per period

Then;

Xi= interest on the amount X for each period

S= Xi(FA, i%, k)

And

X=Si AF, i%, k=S(1+i)k-1

Capitalized Cost = FC + x = FC + S(1+i)k-1

Capitalized Cost = FC + x = FC + S(1+i)k-1

If the property or structure costs ₱B to obtain and it will have to be replaced every k periods for the same amount, Then;

Capitalized Cost = S + x = S + Si AF, i%, k

= Si i +AF, i%, k=Si(AP,i%, k)

Capitalized Cost = S1-(1+i)-k

Capitalized Cost = S1-(1+i)-k

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