## What is Ordinary Annuity?

An Ordinary annuity is 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.

### Examples of Ordinary Annuity

Below are the examples explained in detail.

#### Example #1

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

**Solution:**

- Future Value 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 Interest rate prevailing in the market at 5%, then he will have to deposit 904,873.99 yearly.

#### Example #2

Mr. Y wants to receive 500,000 yearly after retirement for the rest of his life. The interest rate prevailing is said 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 interest rate prevailing in the market. 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 is paying $5000 each month and will pay it for 10 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 Present Value of all the future payments. Now, this value is the intrinsic value of the bond.
- Annuity calculations are also used to calculate EMIs on loans taken. We pay fixed amounts at the end of each month for a fixed tenure. At the beginning of Loan tenure, the EMI consists mostly of Interest component, but as we reach to the end of Tenure, the Interest portion goes down and the principal component gets high.

### Limitations

- It considers that the payment will be fixed throughout the tenure, due to financial distress the default risk is not considered
- Ordinary Annuity always shows the best picture, that is if all the payments are invested at the exact specified interest rate then the outcome will match as per the result.

### Conclusion

An ordinary annuity is an important part of the Financial Market. Pension Schemes, Bank Loans, Bond Markets all depend on annuity calculation. It is simple but extremely important to find the present value of Future Cash Flows.

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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 –

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