**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

** Illustration 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

** Illustration 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?

## 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 for Annuity Due (Annual Discounting)

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

** Illustration 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

** Illustration 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?

## 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

** Illustration 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 MCQs.