Calculation of Present Value of the Various Annuities

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This makes it easier for you to plan for your future and make smart financial decisions.

Introduction to Present Value of an Ordinary Annuity

An annuity is a contract you enter into with a financial company where you pay a premium in exchange for payments later on. The present value of an annuity is the cash value of all of your future annuity payments.


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The rate of return or discount rate is part of the calculation. Thus, the higher the discount rate, the lower the present value of the annuity is. The present value of an annuity is based on the time value of money.

Excel Formula Training

With an annuity, you might be comparing the value of taking a lump sum versus the annuity payments. Calculating the present value of annuity lets you determine which is more valuable to you.

As you may have guessed from the number of variables in the formula, calculating the present value of an annuity can be tricky. We explain in detail how to use the formula below. Using the above formula, you can determine the present value of an annuity and determine if taking a lump sum or an annuity payment is a more efficient option.

Annuity - Overview, Types and Formulas for Valuation of Annuities

Here is an example of how that can work. Note that this formula is for a regular annuity.

What is Present Value of an Annuity?

Alternatively defined, the present value of an annuity is the amount which if invested at the start of first period at the given annual percentage rate will equate the sum of the amount invested and the compound interest earned on the investment with the product of number of the periodic payments and the face value of each payment.

Although the present value PV of an annuity can be calculated by discounting each periodic payment separately to the starting point and then adding up all the discounted figures, it is more convenient to use the following formulas.

Present value of an annuity

Since cash flows occur one period earlier in case of an annuity due, the present value of annuity due can be determined by reversing discounting for one period. The relationship between present value of an ordinary annuity and present value of an annuity due is given by the following expression:. Substituting the expression for present value of ordinary annuity, we get the following equation:.

The interest rate on the investment was Calculate the original investment and the interest earned.


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