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# HP 10b Calculator - Calculating the Present and Future Values of an Annuity that Increases at a Constant Rate at Equal Intervals of Time

## Description

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 of time. Routines are included for both END and BEGIN mode calculations.

## Calculator symbol key

The procedures in this document use the following text to represent symbol keys:
 Key Description Text Representation colored key; shift key SHIFT Divide divide

## Present value of an increasing annuity (End mode)

1. Set END mode (Press SHIFT, then BEG/END if BEGIN annunciator is displayed) and press 1, then SHIFT, then P/YR.
2. Key in the total number of payment periods and press N.
3. Key in the payment percentage increase per period expressed as one plus the decimal interest rate and press SHIFT, STO, 0, then INPUT. (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 SHIFT, %CHG, then I/YR.
5. Key in the amount of the starting payment and press divide, RCL, 0, PMT, 0, then FV.
6. Press PV to calculate the present value of the payment stream.

## Present value of an increasing annuity (Begin mode)

1. Set END mode (Press SHIFT, then BEG/END if BEGIN annunciator is displayed) and press 1, SHIFT, then P/YR.
2. Key in the total number of payment periods and press N.
3. Key in the discount (interest) rate per period expressed as one plus the decimal interest rate and press INPUT.
4. Key in the payment percentage increase per period expressed as one plus the decimal interest rate, and press SHIFT, %CHG, then I/YR.
5. Key in the amount of the starting payment and press PMT, 0, then PV
6. Press FV to calculate the present value of the payment stream.

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

1. Perform steps 1 to 6 of the Present Value of an Increasing Annuity (End Mode) routine above.
2. Press 0, then PMT.
3. Key in the discount (interest) rate as a percentage and press I/YR.
4. Press FV to calculate the future value of the payment stream.

## Future value of an increasing annuity (BEGIN mode)

1. Perform steps 1 to 6 of the Present Value of an Increasing Annuity (Begin Mode) routine above.
2. Press SHIFT, STO, PV, 0, then PMT.
3. Key in the periodic discount (interest) rate as a percentage and press I/YR.
4. Press FV to calculate the future value of the payment stream.

## Example of calculating the present value

Income property that is providing increasing rents can be evaluated. Net rent is received at the end of each year. The first year's rent is expected to be \$8,500 and rent is expected to increase 7 percent each year. Each payment occurs at the end of the year. What is the present value of the estimated income stream over the first 5 years if the discount rate is 17 percent?
Set to END mode. Press SHIFT, then BEG/END if BEGIN annunciator is displayed.
 Key Display Description Press 1, SHIFT, then P/YR 1.00 Sets 1 P/YR Press 5, then N 5.00 5 years Press 1.07, SHIFT, STO, then 0 1.07 Calculates a factor interest rate Press INPUT, 1.12, SHIFT, %CHG, then I/YR 4.67 Stores as I/YR Press 8500, divide, RCL, 0, then PMT 7,943.93 Calculates and stores PMT Press 0, then FV 0.00 Zero as FV Press PV -34,706.26 Calculates PV

## Example of calculating a future value

Today \$1,000 was deposited into a savings account that earns 9 percent interest, compounded annually. The plan is to increase the amount of the deposit by 15 percent each year. How much will accumulate in 20 years?
Set to ENDmode. Press SHIFT, then BEG/END if BEGIN annunciator is displayed.
 Keys Display Description Press 1, SHIFT, then P/YR 1.00 Set P/YR to 1 Press 20, then N 20.00 Store N Press 1.09, then INPUT 1.09 Calculate a factor interest rate Press 1.15, SHIFT, then %CHG 5.50 Press I/YR 5.50 Stores as I/YR Press 1000, then PMT 1,000.00 Calculates intermediate factor Press 0, then PV 0.00 Press FV -34,885.37 Press SHIFT, STO, then PV -34,885.37 Stores as PV Press 0, then PMT 0.00 Press 9, then I/YR 9.00 Stores interest rate Press FV 195,511.97 Calculates future accumulation

Country/Region: United States