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Future Value and Present Value of Ordinary Annuity

In an ordinary annuity, the first cash flow occurs at the end of the first period, and in an annuity due, the first cash flow occurs at the beginning (at time 0).

The present value and future values of these annuities can be calculated using a simple formula or using the calculator.

Future Value of an Ordinary Annuity

Let’s say we have an ordinary annuity that pays $500 every year for the next 5 years. The expected rate of return is 8%. The future value of this annuity can be represented as follows:

ordinary-annuity

This can be calculated using the following formula:

fv-oa

While you can use the above formula to calculate the future value of annuity, you can simply calculate the future value using the BAII Plus calculator. Note that in our example, m = 1, since the compounding frequency is 1.

Calculator usage

Enter PMT = $500, N = 5, I/Y = 8%.

Since compounding frequency is 1, set Number of Compounding Periods (C/Y) to 1by pressing [2nd][P/Y][Down Arrow].

Since it’s an ordinary annuity, we should set End-of-period payments [END]. This can be set by pressing the key [2nd][BGN]

To compute the future value, press the key CPT > FV

FV = $2933.2

Present Value of an Ordinary Annuity

Calculate the present value of an ordinary annuity that pays $500 at the end of each year for the next 5 years. The discount rate is 8%.

This can be calculated using the TVM functions of BAII Plus calculator as follows:

PMT = 500

N = 5

I/Y = 8%

To compute present value, press the key CPT > PV.

PV = 1996.355

Without the calculator, you would calculate this as follows:

pv-oa

PV = 1996.355

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