# 21+ Differences Between Annuity And Perpetuity (Explained)

Life has no meaning without money. Has it? The value of money keeps changing forever. Its value decreases as time passes. The value of today’s \$10,000 hold would hold much less value in upcoming years.

The time value of money is calculated to calculate how much today’s money would value in the future; Annuity and Perpetuity are two concepts used in calculations of the Time Value of Money.

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Key Differences –

Annuity –

1. Annuity means a series of payments for a fixed period. Payments in Annuities are paid as well as received.
2. Annuities are of two types, namely Ordinary Annuity and Annuity Due.
3. It is possible to calculate the future value and present value of an Annuity.
4. Compound interest is used to calculate the present and future value of an Annuity.

Perpetuity –

1. Perpetuity means a series of payments for an infinite period.
2. Payments in Perpetuities are only received.
3. There are two types of Perpetuities: Flat (or Constant) Perpetuity and Growth Perpetuity.
4. It is only possible to calculate the present value of a perpetuity. Its future value can not be calculated.
5. Simple Interest is used to calculate the present value of a Perpetuity.

## Major Differences Between Annuity And Perpetuity

To understand what an Annuity and a Perpetuity are, it is essential to understand what Time Value of Money is.

### What exactly is the Time Value of Money?

The time value of money is an important concept that states that money today is valued more than it would tomorrow.

Remember how much \$10,000 could buy at your parents’ time? Can it buy the same amount of things today? That is the Time Value of Money which states money today has more value than the same money tomorrow.

Time Value of Money and Investment Decisions –

What would you choose if you were to choose between receiving a huge sum of money today and receiving a huge sum of money ten years later? Simple, receiving today. But why?

Not only will the value of money decrease ten years later, but you can also now invest this money and receive additional Interest. However, you can not have that additional income (Interest) if you receive money years later than today.

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The formula of Time Value of Money –

FV = PV * [1+i/N]^N*T,

Where FV = Future value of money

PV = Present value of money

i = Rate of Interest

N = number of compounding periods per year

T = number of years

### What exactly is Annuity?

Annuities are regular payments that are made for a fixed period. Annuities are usually contracts between two parties, where one pays payments for a fixed period of time and receives the full amount plus Interest after finishing that period.

Annuities are of two types, namely Ordinary Annuity and Annuity due. Ordinary Annuities are those annuities where payments are made at the beginning of every month.

Annuity Due, on the other hand, are those types of annuities where the payments are made at the end of every month.

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Formulas for calculating Annuities are –

–         Ordinary Annuity – Annuity = r * PVA Ordinary / [1 – (1 + r)-n]

–         Annuity Due – r * PVA Due / [{1 – (1 + r)-n} * (1 + r)]

Here,

PVA Ordinary = Present Value of Ordinary Annuity,

PVA Due = Present Value of Annuity Due,

r = Interest rate,

n = number of periods.

• Present value of an Annuity = PV = P×(1−(1+r)-n) / r
• Future value of an Annuity = FV = P×((1+r)n−1) / r

Here,

P = Sum of each payment,

r = Interest rate/ period,

n = total number of periods.

### What exactly is Perpetuity?

Perpetuities are annuities that involve making fixed payments, but in perpetuities, payments are made for infinite periods. Every Perpetuity is an annuity, but annuities are not perpetuities.

There are mainly two types of perpetuities, namely Flat or Constant Perpetuity and Growth Perpetuity. Constant Perpetuity is that Perpetuity that stays the same throughout.

It involves payment of a fixed Sum. On the other hand, Growth Perpetuity is the Perpetuity where the payment sum increases yearly.

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Formulas for calculating Perpetuities are –

Constant Perpetuity – PV = A/R

Growth Perpetuity – PV = A/R – G

Here,

A = Amount,

R = Interest rate,

G = Growth Rate.

## Contrast Between Annuity And Perpetuity

### Origin of The Word

• Annuity: The word Annuity originated from the Latin word “annus,” which means “Year.”
• Perpetuity: The word Perpetuity originated from the Latin word “perpetuus,” which means “Continuing throughout.”

### Meaning

• Annuity: Annuity refers to several payments made for a finite period.
• Perpetuity: Perpetuity is an annuity that refers to several payments made for an infinite period.

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All Perpetuities are Annuities, but not all annuities are Perpetuities –

Perpetuities are a type of Annuities as Annuities mean making payments at a fixed interval of time. But this does not mean all Perpetuities are Annuities, as Perpetuities involve making payments for an infinite period, and Annuities involve making periods for a finite period. Thus, All Perpetuities are Annuities, but not all annuities are Perpetuities.

### Duration

• Annuity – Annuities are made for a finite period.
• Perpetuity: Perpetuities are made for an infinite period.

### Present And Future Value

• Annuity: The present and future values can be calculated for an annuity.
• Perpetuity: Only the present value can be calculated for Perpetuity.

### Types

• Annuity: Annuities are of two types: Ordinary Annuity and Annuity Due.
• Perpetuity: Perpetuities are also of two types, namely Flat/ Constant Perpetuity and Growth Perpetuity.

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Types of Annuities and Perpetuities –

Annuities –

1. Ordinary Annuity – Ordinary Annuities are those annuities whose payments are made at the beginning of every month.
2. Annuity Due – As the name suggests, Annuity Due are those payments whose payments are made at the end of every month.

Perpetuities –

1. Constant or Flat Perpetuities – Constant or Flat Perpetuities are those perpetuities whose payment amount stays the same.
2. Growth Perpetuities – Growth Perpetuities are those Perpetuities whose payment amount increases by a small amount every time.

### Interest Type

• Annuity – Compound Interest is used in Annuities.
• Perpetuity – Simple Interest is used in Perpetuities.

### Suitable For

• Annuity: Annuities are suitable for those who want a source of income for a fixed period.
• Perpetuity: Perpetuities are suitable for those who want to pass on their legacy to their younger generations.

Formula –

Annuity: Formulas for calculating Annuities are –

–         Ordinary Annuity – Annuity = r * PVA Ordinary / [1 – (1 + r)-n]

–         Annuity Due – r * PVA Due / [{1 – (1 + r)-n} * (1 + r)]

–         Present Value of an Annuity = PV = P×(1−(1+r)-n) / r

–         Future Value of an Annuity = FV = P×((1+r)n−1) / r

Perpetuity – Formulas for calculating Perpetuities are –

–         Constant Perpetuity – PV = A/R

–         Growth Perpetuity – PV = A/R – G

Example –

Annuity – Examples of Annuity are Life insurance, EMIs, Rent, etc.

Perpetuity – Examples of Perpetuity are Consoles, Contracts, irredeemable preference share dividends, etc.

## Conclusion

Annuity and Perpetuity are the two most important financial terms involving regular payments. Annuity involves regular payments of a sum of money for a finite period. On the other hand, Perpetuity involves regular payments of a sum of money for an infinite period.

#### Q1. What is meant by the Time Value of Money?

Time Value of Money is a concept that states that money today has more value than money tomorrow.

Therefore, according to the Time Value of Money, the value of money keeps on decreasing as time goes by.

#### Q2. What are the major differences between an Annuity and a Perpetuity?

The major differences between Annuity and Perpetuity are –

1. Annuity involves making payments at a regular interval for a finite period, whereas Perpetuity involves making payments at a regular interval but for an infinite period.
2. The present and future values can be calculated for annuities, but only the present value can be calculated for perpetuities.
Annuities use compounded Interest, while perpetuities use simple Interest.
3. Annuities are of two types: Ordinary Annuity and Annuity Due, and the types of Perpetuity include Constant Perpetuity and Growth Perpetuity.

#### Q3. What is the difference between Ordinary Annuity and Annuity Due?

The main difference between an Ordinary Annuity and Annuity Due is that the former involves making payments at the beginning of every month while the latter involves making payments at the end of every month.

#### Q4. What are the formulas for Annuities?

The formulas for annuities are as follows

–         Ordinary Annuity – Annuity = r * PVA Ordinary / [1 – (1 + r)-n]
–         Annuity Due – r * PVA Due / [{1 – (1 + r)-n} * (1 + r)]
–         Present Value of an Annuity = PV = P×(1−(1+r)-n) / r
–         Future Value of an Annuity = FV = P×((1+r)n−1) / r

#### Q5. What is the difference between Flat Perpetuity and Growth Perpetuity?

The main difference between Flat or Constant Perpetuity and Growth Perpetuity is that the former involves making fixed or the same payments throughout, while the latter makes payments whose amounts increase yearly.

#### Q6. What are the formulas for calculating Perpetuities?

The formulas for calculating perpetuities are as follows

–         Constant Perpetuity – PV = A/R
–         Growth Perpetuity – PV = A/R – G