# 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).

1. Press the f key, FIN and press the g key, END.
2. Key in the total number of payment periods and press the n key.
3. 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).
4. 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.
5. Key in the amount of the starting payment and press x<>y, DIVIDE, PMT.
6. Press PV to calculate the present value of the payment stream.

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

1. Press the f key, FIN and press the g key, END.
2. Key in the total number of payment periods and press the n key.
3. Key in the discount interest rate per period expressed as one plus the decimal interest rate and press ENTER.
4. 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.
5. Key in the amount of the starting payment and press PMT.
6. Press FV to calculate the present value of the payment stream.

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

1. Press the f key, FIN, and press the g key, END.
2. Key in the total number of payment periods and press the n key.
3. 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).
4. 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.
5. Key in the starting payment amount and press x<>y, DIVIDE, PMT.
6. Press PV, type in 0, press PMT.
7. Key in the discount interest rate as a percentage and press the i key.
8. Press FV to calculate the future value of the payment stream.

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

1. Press the f key, FIN and the g key, END.
2. Key in the total number of payment periods and press the n key.
3. Key in the discount (interest) rate increase per period expressed as one plus the decimal interest rate and press ENTER.
4. 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.
5. Key in the starting payment amount and press PMT.
6. Press FV, STO, PV, Type in 0, press PMT.
7. Key in the periodic discount interest rate as a percentage and press the i key.
8. 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

8500, x<>y, DIVIDE, PMT

7,943.93

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.