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# Difference between Annuity and Perpetuity

Annuity and Perpetuity are financial plans. It is used in financial markets. It is vital to know about Annuity and Perpetuity. Let’s dive deeper to get a broad spectrum of these concepts.

## What is Annuity?

The word *annuity* is derived from the Latin word *annus* which means *year*. An annuity is a
financial product. Annuities are the regular payments of fixed principle for a precise period of
time. The time period followed is as per the terms and conditions in the agreement which the
parties have called a deal.

### Example

Employer A and employee B have made a deal that states that B will receive a fixed salary for a fixed period of time before getting a hike of 92%. Hence, B receives a fixed salary for 3years before getting this hike. The financial plan followed for these 3 years is Annuity.

The concurring annuity or future value of an annuity is calculated by using the compound interest formula, i.e.,

$$\mathrm{\mathit{A}\:=\:\mathit{P} \mathrm{\left ( 1+\frac{\mathit{R}}{\mathit{N}} \right )}^{\mathit{NT}}}$$

Where A is the annuity or compound interest, P is the principle, R is the interest rate, N is the number of years, and T is the number time periods.

There are two types of annuity, they are − a) Ordinary Annuity and b) Annuity Due.

In an Ordinary Annuity, regular payments are done at the start of the time period.

In an Annuity Due, regular payments are done at the end of the time period.

There are also other types of Annuities −

Fixed Annuity, where an annuity is paid or received for a fixed time.

Variable Annuity, where actually one owns the investment and returns as it depends on how well the underlying subaccounts perform.

Indexed Annuity, refers to the payments on returns on the stocks. It performs well when the Stock market performs well. It is called a fixed-index or variable-index annuity. It is also called a hybrid of Fixed and Variable annuity.

Annuities are used in banks, insurance, EMI, Savings account, FD accounts and RD accounts, monthly home mortgage payments, pensions, and many more.

### Merits and Demerits of Annuity

Following are the Merits of Annuity −

With the continuous inflow of fixed money for a fixed period of time, hence there will be no delay in payments and there will be no financial insecurity.

Annuity is planned considering inflation, health insurance, everyday expenses, and more.

Most of the time annuity plans provide Tax Exemption.

In an annuity, the principle is fixed and one can invest by entrusting on the fact that their investment or principle will be returned to them.

Following are the Demerits of Annuity −

Annuity is complicated. Not everyone can understand and follow it with ease.

Annuity does not allow the withdrawal of money until the end of the fixed time. If it allows withdrawing the money in half path or before the term ends, it will be possible only on serious terms and conditions.

Variable Annuities are very expensive.

The returns on invested money in the annuity will be taxed.

## What is Perpetuity?

The word *perpetuity* is derived from the Latin word *perpetuus* which means *continuing
throughout*. Perpetuity is referred to as an annuity or regular inflows of fixed principle
throughout the lifetime, infinite years without a fixed period of time. It is also known as
Perpetual Annuity. For example, a pension paid to retired soldiers is perpetuity as they are paid a
pension throughout their lifetime.

Perpetuity is an ordinary annuity, as perpetuity is a form of annuity which is received for infinite years. Perpetuity is used in stocks, bonds, real estate, pensions, and many more. Perpetuity is calculated by doing Simple Interest, i.e., PV= C/R where PV is Present Value, C is the Amount of continuous cashflows and R is Rate of Interest. As perpetuity is paid throughout a lifetime its future value cannot be calculated. Primarily a principle is decided which will be paid throughout life, and this fixed money with interest is paid or received periodically.

Perpetuity is divided into two types −

Constant Perpetuity − It is fixed forever. No changes in the sum of money received.

Example − Bonds, and Pension.

Growing Perpetuity − It keeps growing as per the stock market. Perpetuity changes.

Example − Real Estate.

### Formula

The formula of Constant Perpetuity: PV=C/R, i.e., PV is Present value, C is cash flow and R is Rate of Interest.

The formula of Growing Perpetuity: PV=C/R-G, i.e., PV is Present Value, C is cash flow, R is Rate of Interest, and G is Growth Rate.

### Merits and Demerits of Perpetuity

Following are the Merits of Perpetuity −

The concept of Perpetuity is simple; it can be comprehended easily.

Perpetuity offers financial security and social security since perpetuity is received throughout one’s life.

Perpetuity offers better and more beneficial investments. If one faces losses in stocks, there will be a financial backup. It is prosperous when compared to other bonds.

Perpetuity is less expensive compared to Annuity and any other bond as it does not have fixed years which exists in annuity and other bonds.

Following are the Demerits of Perpetuity −

It is almost impossible and onerous to calculate the face value of perpetuity since there is no fixed number of years.

It is not beneficial as it does not allow investing interest money anywhere else.

It is not a better choice in the long run since one cannot withdraw the money.

## Difference between Annity and Perpetuity

The following comparison table will help you to have a brief understanding and get clarity between Annuity and Perpetuity −

Characteristics | Annuity | Perpetuity |
---|---|---|

Definition | Regular payment for a fixed period
of time. | Regular payment for infinite
time. |

Duration | The duration is limited. | The duration is infinite, it is not
limited. |

Types | There are two types; Ordinary
Annuity and Annuity Due. | No types in perpetuity. |

Method | Payment is paid or received. | Payment is received. |

Calculation | Annuity is calculated by doing
Compound Interest. | Perpetuity is calculated by doing
Simple Interest. |

Future value | Future Value can be calculated. | Future value cannot be
calculated. |

Example | Insurance, EMI | Pension, Scholarship, Constant
Dividend. |

## Conclusion

After comprehending the above information, we can easily differentiate the difference between annuity and perpetuity, that is, their time limit. An annuity is the fixed face value that is paid regularly for fixed numbers of years, while perpetuity is a perpetual annuity, that is, the annuity which is paid *perpetually* or for an infinite time.

Calculations done for the annuity are complex, while calculations done for perpetuity are simple. An annuity is easy to understand, while perpetuity is difficult to understand, and so is its future value, an annuity’s future value can be calculated while for perpetuity, it is almost not possible.

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