- Introduction - Time Value of Money
- Interest Rates
- Interest Rate Equation
- Nominal Interest Rate and Effective Yield
- Time Value of Money for Different Compounding Frequencies
- Future Value of a Single Cash Flow
- Present Value of a Single Cash Flow
- Future Value and Present Value of Ordinary Annuity
- Present Value and Future Value of Annuity Due
- Present Value of a Perpetuity
- Present Value and Future Value of Uneven Cash Flows
- Annuities with Different Compounding Frequencies
- Using a Timeline to Solve Time Value of Money Problems

# Future Value and Present Value of Ordinary Annuity

An annuity refers to a series of equal cash flows that occur periodically such as monthly, quarterly or annually. For example, an investment that gives you fixed monthly payments for a specified period. There are two types of annuities, namely, ordinary annuities and annuities due. .

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:

This can be calculated using the following formula:

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 = 1996.355

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