Ordinary Annuity

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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.

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  • 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

  1. 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 [wsm-tooltip header="Present Value" description="Present Value (PV) is the today's value of money you expect to get from future income. It is computed as the sum of future investment returns discounted at a certain rate of return expectation." of all future payments. Now, this value is the intrinsic value of the bond.
  2. 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 the Interest component, but as we reach the end of the 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. If all the payments are invested at the specified interest rate, then the outcome will match the result.

Conclusion

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

Frequently Asked Questions (FAQs)

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.