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# Present Value of Annuity

Present Value of Annuity is a series of constant cash Flows (CCF) over limited period of time say monthly rent, installment payments, lease rental. There are two types of Annuity:

## Ordinary Annuity or Deferred Annuity

If constant cash flow occur at the end of each period/year. Payment of car loan, mortgage loan and student loan are examples of ordinary annuity ## Present Value for Ordinary Annuity (Annual Discounting)

The value of annuity at present time evaluated at a given interest rate assuming that discounting take place one time in a year (Annually). Two methods for calculation: ## Formula ## Example # 1:

You want to buy an ordinary annuity that will pay you \$1,000 a year for the next 5 year. You expect annual interest rates will be 7 percent over that time period. What is maximum price you would be willing to pay today?   ## Present Value for Ordinary Annuity (Intra Year Discounting)

The value of annuity at present time evaluated at a given interest rate assuming that discounting take place more than one time in a year (Intra Year). Interest rate reduced while periods of time increase by frequency of compounding (m) i.e. i/m and n*m. Two methods for calculation: ## Formula ## Example # 2:

Mr. Bengish has signed a contract which pays him \$100,000 per year for five years. Using a discount rate of 8% and discounting take place semi-annually, what is the present value of his contract?  >> Practice Present Value of Annuity MCQs.

## Annuity Due

If payments or receipts are made at the beginning of each year/period, the annuity is an annuity due. Rental payment for apartment and life insurance payments are typical example of this annuity. ## Present Value of Annuity Due (Annual Discounting)

Present value of annuity due  is the value of annuity due at present time evaluated at a given interest rate assuming that discounting take place one time in a year (Annually)

Two methods for calculation ## Formula  ## Example # 3:

What is the value today of a 5-year annuity due that pays \$1,000 a year assuming that rate is 7%?   ## Present Value for Annuity Due (Intra-year Discounting)

The value of annuity due at present time evaluated at a given interest rate assuming that discounting take place more than one time in a year (Intra-year). Interest rate reduced while periods of time increase by frequency of compounding (m) i.e. i/m and n*m. Two methods for calculation ## Formula ## Example # 4:

Find the present value of due annuity with periodic payments of \$3,000, for a period of 5 years at an interest rate of 16%, discounted quarterly?  >>> Practice Present Value of Annuity MCQs.

## When time n is unknown (Annually)

In situation if we have future value and present value of lump sum with interest rate, than we can find time ## Example # 5:

You need to accumulate \$10,000. To do so, you plan to make deposits of \$1,250 per year, with the first payment being made a year from today, in a bank account which pays 12 % interest, compounded annually. Your last deposit will be less than \$1,250 if less is needed to round out to \$10,000.  How many years will it take you to reach your \$10,000 goal, and how large will the last deposit be? >> Practice Present Value of Annuity Quiz 1.

## References

Financial Management: Theory and Practice, Dr Eugene F Brigham & C Micheal Ehrhardt

Fundamentals of Financial Management: Concise Edition, Brigham Houston

The Economist Guide to Financial Management, John Tennet

Financial Management: Core Concepts, Raymond M Brooks

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