**Introduction**

The following routines can be used to calculate the present and future values of an annuity that increases at a constant rate at equal intervals. Routines are included for both END and BEGIN mode calculations.

**Instructions**

The instructions are given below for calculating both present and future values of an increasing annuity, each in END Mode and BEGIN Mode.

### Present value of an increasing annuity (END Mode).

- Press the
**f**key,**FIN**and press the**g**key,**END**. - Key in the total number of payment periods and press the
**n**key. - Key in the payment percentage increase per period expressed as one plus the decimal interest rate and press
**ENTER**. (If there is a percentage decrease, key it in as one minus the decimal interest rate). - Key in the discount interest rate per period expressed as one plus the decimal interest rate and press the
**DELTA_**key, then the**i**key. - Key in the amount of the starting payment and press
**x<>y**,**DIVIDE**,**PMT**. - Press
**PV**to calculate the present value of the payment stream.

### Present value of an increasing annuity (BEGIN Mode)

- Press the
**f**key,**FIN**and press the**g**key,**END**. - Key in the total number of payment periods and press the
**n**key. - Key in the discount interest rate per period expressed as one plus the decimal interest rate and press
**ENTER**. - Key in the payment percentage increase per period expressed as one plus the decimal interest rate and press the
**DELTA_**key, then the**i**key. - Key in the amount of the starting payment and press
**PMT**. - Press
**FV**to calculate the present value of the payment stream.

### Future value of an increasing annuity (END Mode)

- Press the
**f**key,**FIN**, and press the**g**key,**END**. - Key in the total number of payment periods and press the
**n**key. - Key in the payment percentage increase per period expressed as one plus the decimal interest rate and press
**ENTER**. (If there is a percentage decrease, key it in as one minus the decimal interest rate). - Key in the discount interest rate per period expressed as one plus the decimal interest rate and press the
**DELTA_**key, then the**i**key. - Key in the starting payment amount and press
**x<>y**,**DIVIDE**,**PMT**. - Press
**PV**, type in**0**, press**PMT**. - Key in the discount interest rate as a percentage and press the
**i**key. - Press
**FV**to calculate the future value of the payment stream.

### Future value of an increasing annuity (BEGIN Mode).

- Press the
**f**key,**FIN**and the**g**key,**END**. - Key in the total number of payment periods and press the
**n**key. - Key in the discount (interest) rate increase per period expressed as one plus the decimal interest rate and press
**ENTER**. - Key in the payment percentage increase per period expressed as one plus the decimal interest rate and press the
**DELTA_**key, then the**i**key. - Key in the starting payment amount and press
**PMT**. - Press
**FV**,**STO**,**PV**, Type in**0**, press**PMT**. - Key in the periodic discount interest rate as a percentage and press the
**i**key. - Press
**FV**to calculate the future value of the payment stream.

**Examples**

Following are two examples of increasing annuity calculations.

### Example 1

You are appraising a piece of income property that is providing increasing rents. Assuming a 7% rate of increase over the next 5 years, what is the present value of the income stream? Your discount rate is 12%, rent for the first year is expected to be $8,500, and the payments occur at the end of the year.

Keystrokes | Display | Description |
---|---|---|

f, FIN, g, END | 0.00 | Clears financial registers. |

5, n | 5.00 | Stores number of payments. |

1.07, ENTER | 1.07 | Enters increase rate plus 1. |

1.12, DELTA_, i | 4.67 | Stores adjusted rate into i. |

8500, x<>y, DIVIDE, PMT | 7,943.93 | Stores adjusted payment. |

PV | -34,706.26 | Calculates present value. |

### Example 2

Today you deposit $1000 into a savings account that earns 9 1/2 % interest, compounded annually. Each year you plan to increase the amount of your deposit by 15%. How much will you accumulate in 20 years?

Keystrokes | Display | Description |
---|---|---|

f, FIN, g, END | 0.00 | Clears the financial registers. |

20, n | 20.00 | Stores the number of payments. |

1.095, ENTER | 1.10 | Enters the increase rate plus 1. |

1.15, DELTA_, i | 5.02 | Stores the adjusted rate into i. |

1000, PMT | 1,000.00 | Stores the starting payment. |

FV, STO, PV | -33,145.85 | |

0, PMT | 0.00 | |

9.5, i, FV | 203,568.97 | Calculated future value. |

Updated On: 12.09.20