# Ordinary Annuity

Last Updated :

21 Aug, 2024

Blog Author :

N/A

Edited by :

N/A

Reviewed by :

Dheeraj Vaidya

Table Of Contents

## What is Ordinary Annuity?

An Ordinary annuity is a fixed payment made at the end of equal intervals (Semi-annually, Quarterly or monthly), which is mostly used to calculate the present value of fixed payment paying securities like Bonds, Preferred shares, pension schemes, etc.

##### Table of contents

- An ordinary annuity is a set payment delivered at the end of equal intervals (semi-annually, quarterly, or monthly), and it is commonly used to determine the present value of fixed-payment securities such as bonds, preferred shares, pension plans, and so on.
- The present value of long-term fixed-paying bonds is calculated using ordinary annuity calculations.
- An ordinary annuity is a vital component of the financial market. For example, annuity calculations are used in pension plans, bank loans, and bond markets.

### Examples of Ordinary Annuity

Below are the examples explained in detail.

#### Example #1

Mr. X wants to make a corpus of $5 million after five years with the Interest rate prevailing in the market at @5%. Mr. X wants to make yearly payments.

**Solution:**

- Future Va,lue of Ordinary Annuity = Annuity Payment (1 + Periodic Interest Rate)
^{Number Of Periods * Number of years} - 5,000,000 = Annuity Payment ( 1 + 0.05)
^{n }+ Annuity Payment ( 1 + 0.05)^{n-1}+ …… Annuity Payment ( 1 + 0.05)^{n-4} - Annuity Payment =
**$904,873.99**

So, If Mr. X wants to make a corpus of $5 million after 5 Years with an Interest rate prevailing in the market at 5%, then he will have to deposit 904,873.99 yearly.

#### Example #2

**Example #2**

Mr. Y wants to receive 500,000 yearly after retirement for the rest of his life. The interest rate prevailing is 5%. So how much will Mr. X have to save till retirement so that he can achieve his goal?

**Solution:**

- 500,000/0.05 =
**$10,000,000**

So Mr. Y will have to save 10 million dollars till retirement so that he can withdraw 500,000 each year till death.

#### Example #3

A Bond will pay 5 million Dollars after 5 Years. Each Year it will pay 5% interest on Face Value. The rate prevailing in the market is 4%. What should be the price of the Bond now?

**Solution: **

- Payment made by bond each year – 5% on 5 million = 250000
- Discount Rate = 4%
- Number of Years = 5
- Face Value received at the end of 10 Years = 5,000,000

**Price of the Bond today = Present Value of Ordinary Annuity**

- = 250,000/(1 +0.04)
^{1}+ 250000/(1 +0.04)^{2 }+ 250,000/(1 +0.04)^{3}+ 250,000/(1 +0.04)^{4 }+ 5,250,000/(1+0.04)^{5} **= $5,222,591.117**

So, you can see that the Face value of the Bond is 5 million, but it is trading at a premium because the rate the bond is offering, i.e., 5%, is more than the rate the market is offering, i.e., 4%. So, the market is ready to pay more for a bond that is paying more than the prevailing interest rate. So it is trading at a premium.

### Uses of Ordinary Annuity

- Ordinary Annuity calculations are used to
**calculate the present value**of long-term fixed-paying Bonds. Say a bond pays $5000 each month and will pay it for ten years. So to calculate the present value of the bond, we use annuity calculation. Each $5000 will be discounted with the prevailing interest rate in the market, and we will get the }}," "],"answer":,"jsonQuestion":"\u003cstrong\u003e1. What is a simple and ordinary annuity?\u003c/strong\u003e ","jsonAnswer":"A simple annuity pertains to a sequence of consistent payments issued at periodic intervals. For instance, think of regular monthly rent payments. Conversely, an ordinary annuity shares similarities yet diverges in timing. Here, payments transpire at the conclusion of each interval, mirroring scenarios like annual interest disbursements."},{"id":"faq-question-1692861957957","question":}}," "],"answer":,"jsonQuestion":"\u003cstrong\u003e2. What is an ordinary annuity called?\u003c/strong\u003e ","jsonAnswer":"Ordinary annuity assumes the alias of an \u0022annuity in arrears.\u0022 This terminology stems from the timing of payments occurring at the culmination of each designated period. In financial discussions, this term succinctly captures the deferred nature of the payment schedule."},{"id":"faq-question-1692861959154","question":}}," "],"answer":,"jsonQuestion":"\u003cstrong\u003e3. How is the concept of time important in understanding ordinary annuities?\u003c/strong\u003e ","jsonAnswer":"Time plays a crucial role in ordinary annuities. The timing of payments affects the present value calculation, as a dollar received sooner is worth more than the same dollar received later due to factors like interest and inflation."}]} -->**1. What is a simple and ordinary annuity?**A simple annuity pertains to a sequence of consistent payments issued at periodic intervals. For instance, think of regular monthly rent payments. Conversely, an ordinary annuity shares similarities yet diverges in timing. Here, payments transpire at the conclusion of each interval, mirroring scenarios like annual interest disbursements.

**2. What is an ordinary annuity called?**Ordinary annuity assumes the alias of an "annuity in arrears." This terminology stems from the timing of payments occurring at the culmination of each designated period. In financial discussions, this term succinctly captures the deferred nature of the payment schedule.

**3. How is the concept of time important in understanding ordinary annuities?**Time plays a crucial role in ordinary annuities. The timing of payments affects the present value calculation, as a dollar received sooner is worth more than the same dollar received later due to factors like interest and inflation.

### Recommended Articles

This has been a guide to Ordinary annuity and its definition. Here we discuss examples of an ordinary annuity with present value and future value calculations, uses, and limitations. You can learn more about financing from the following articles –