- 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

# Present Value and Future Value of Annuity Due

In an annuity due, the first cash flow occurs at the beginning (at time 0). We can use our BA II Plus calculator to calculate the present value and future value of the annuity due using the same procedure as above, just by making one minor adjustment.

*By default the payment period in the calculator is set to END (End-of-period payments). However, for annuity due, the payment occurs at the beginning of the period. So, we need to change the payment period to the beginning BGN (Beginning-of-period payments). To make this change, follow the following steps:*

*On your calculator, press: [2ND][BGN][2ND][SET]*

*The mode is now changed to BGN and you will see BGN displayed on the upper right corner of the display.*

*To switch back to END mode, repeat the above steps. Once the mode is changed, BGN will disappear from the screen.*

We will use the same examples as we used for ordinary annuity and calculate the PV and FV of the annuity due.

**Future Value of an Annuity Due**

An annuity due pays $500 every year for the next 5 years. The expected rate of return is 8%. The future value of this annuity can be calculated as follows:

Calculator Usage |

Since it’s an annuity due, we should set payment period to beginning-of-period payments [BGN].Enter PMT = $500, N = 5, I/Y = 8%.Since compounding frequency is 1, set Number of Compounding Periods (C/Y) to 1 by pressing [2nd][P/Y][Down Arrow].To compute the future value, press the key CPT > FVFV = $3167.965 |

**Present Value of an Annuity Due**

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%.

Calculator Usage |

This can be calculated using the TVM functions of BA II Plus calculator as follows:PMT = 500N = 5I/Y = 8%To compute present value, press the key CPT > PV.PV = $2,156.063 |

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