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## HP 40gs Graphing Calculator - Sinking Fund

The finance aplet

The HP 40gs has a financial solver aplet built into the calculator. To access this aplet, press . Scroll down the list using the key until 'Finance' is highlighted in the display as shown below.

**Figure : Selecting Finance**

Press to begin the aplet. A data entry form is then displayed that is used to solve a number of financial math problems.

**Figure : Displaying the data entry form**

To solve problems using this display, move the cursor using the keys to each field and input its value, if known. To solve for the unknown value, move the cursor to the field for which you wish to solve, and press menu key labeled . The value of the unknown will be calculated and displayed in the field.

## note:

If you enter the aplet and values are already present in some of the fields, you can clear these values to their default state by pressing the WHITE key and then , to access the function written above it.

Several values are already present on this screen. The number of payments per year is set to 12 for monthly compounding, as shown to the right of the 'P/YR:' in the screen above. If annual compounding is desired, this value should be changed to 1. If quarterly compounding is desired, this value should be changed to 4. Just below the 'P/YR:' field, the calculator displays the word 'END', signifying that payments are assumed to occur at the end of each period, which would be the case for ordinary annuities. If payments are desired at the beginning of the period, as would be the case in an annuity due, this value can be changed by moving the cursor to this field. When the cursor is on this field, is displayed above the second menu key, indicating the calculator will supply a list of choices (Begin or End) in a small CHOOSE box if this key is pressed.

## note:

Begin will be displayed as 'Beg' if chosen. To exit from this data entry screen, press a key that starts another function.

**Figure : Displaying the word 'END'**

The HP 40gs Financial solver follows the standard convention that money in is considered positive and money out is negative.

Sinking funds

A sinking fund is an annuity where a specific value in the future is needed, which is accumulated through a series of regular payments. These types of problems often occur when saving for a goal, such as retirement or college tuition.

Practice solving for payment required to achieve a goal

Example 1

How much would you need to save at the end of every month to accumulate $10,000 in 6 years? Assume the funds
would earn 6%, compounded monthly, and that you begin with nothing in the account.

Solution

(press until the 'Finance' aplet is highlighted)

**Figure : Calculating the monthly amount**

Answer

The monthly amount required is $115.73.

Example 2

John wants to retire as a millionaire. He is 25 years old. How much would he need to deposit each month beginning
one month from now and continuing until his 65

^{th}birthday in order to achieve his goal? Assume the funds would earn 5%, compounded monthly, and that John begins with nothing in the account.
Solution

Since John is 25, he has (65 – 25) x 12, or 480 months until his 65

^{th}birthday.
(press until the 'Finance' aplet is highlighted)

**Figure : Calculating the amount to be deposited**

Answer

The amount required to be deposited every month is $655.30.

Example 3

How much money should you deposit each year into an account, beginning one year from today, to have $30,000 in
the account after 15 years? Assume the funds would earn 6%, compounded annually, and that the account begins
with a balance of $1,000.

Solution

(press until the 'Finance' aplet is highlighted)

**Figure : Calculating the amount to be deposited each year**

Answer

The amount to be deposited each year is $1,185.92.

Example 4

How much money should you deposit each month into an account, beginning one month from today, to have
$30,000 in the account after 15 years? Assume the funds would earn 6%, compounded monthly, and that
the account begins with a balance of $100.

Solution

(press until the 'Finance' aplet is highlighted)

**Figure : Calculating the amount to be deposited**

Answer

The monthly amount to be deposited is $102.31.

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