# HP 12c (platinum) - Increasing Annuities

## 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.