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# HP 48 and 49g Series Calculators - Time Value of Money (TVM) Calculation

Introduction
Many financial problems are based on the concept of charging a fee (interest) for the use of someone else's money for a fixed period of time. The phrase time value of money describes the calculations based on such problems.
There are two main types of problem:
• Compound interest
• Simple interest
With simple interest, only the principal (the original amount of money) earns interest for the entire life of the transaction. The principal, plus interest earned, is repaid in one lump sum.
When simple interest is added to the principal at specified compounding intervals, and thereafter, also earns interest, the interest is compounded. Savings accounts, mortgages and leases are compound-interest calculations.
TVM elements
There are five standard variables used to describe most compound interest (TVM) problems:
 n Number of payments I%YR Annual interest rate PV Present value PMT Payment amount each period (periodic payment amount) FV Future value BEG/END Whether the payment is made at the beginning or end of the payment period
The TVM capability in the calculator does many compound-interest problems. Specifically, the TVM functionality can be used for a series of cash flows (money paid, or money received) when:
• The dollar amount is the same each payment
• The payments occur at regular intervals
• The payment period coincides with the compounding periods
Given any four of the above key elements, it is possible to solve for the fifth variable.
Cash flow diagrams and signs of numbers
It is often helpful to illustrate or visualize TVM calculations with cash-flow diagrams. Cash-flow diagrams are time lines divided into equal segments called compounding (payment) periods. Arrows show the occurrence of cash flows (payment in or out).
Money received is a positive number shown as an arrow pointing up, and money paid out is a negative number shown as an arrow pointing down (Figure 1).
It is essential to use the correct sign (positive or negative) for TVM numbers. The calculations will only make sense if payments out are consistently shown as negative, and payments in (receipts) as positive. A calculation must be performed from the point of view of either the lender (investor) or the borrower, but not both. This is called the TVM sign convention.
Entering TVM calculations
1. Start the financial solver application.
• For the HP 48G series, press and release the turquoise right-pointing shift key, then press SOLVE (on the 7 key) to open the financial solver. The Time Value of Money input form is now displayed.
• For the HP 49G series and 48G II, press and release the blue left-pointing shift key, then press FINANCE (on the 9 key) to open the financial solver. The Time Value of Money input form is now displayed.
2. Depending on the value to be calculated, enter values into the fields.
• To enter a value in a field, place the cursor in the field, enter the value and press ENTER. The value appears in the highlighted field.
• To skip the field for the value being solved for, use the arrow keys.
• To edit an existing value, place the cursor in the field and press [F1] to select EDIT. Edit the value on the command line and press ENTER.
• To specify whether payments are made at the beginning or the end of the payment period, place the highlight in the Beg/End field and press [F2] to select CHOOS. (The Beg/End field is immediately below the P/YR field. It displays either Beg or End.) Select the value you want from the list.
TVM example
Example: A home mortgage
The maximum monthly mortgage repayment you can make is \$850. You can make a \$14,000 down payment. The current interest rate is 8.75%
For a mortgage of 25 years, what is the maximum purchase price that you can afford?
Figure : Cash flow diagram
Following are the keystrokes used to solve the problem in this example problem:
• On the HP 48G series, press and release the turquoise right-pointing shift key, then press [SOLVE].
• On the HP 49G series and 48G II, press and release the blue left-pointing shift key, then press [FINANCE].
 TVM entry field Keystrokes Field display Notes n 300, then ENTER 300.00 Number of payments I%YR 8.75, then ENTER 8.75 Annual interest rate PV Move right No change Skip amount to borrow field PMT 850, [+/-], then ENTER -850.00 Monthly payment P/YR 12, then ENTER 12 Number of payments per year FV 0, then ENTER 0.00 Future value = 0 (i.e. mortgage paid off) Beg or End If End move right. If Beg, [F2], arrow down to End, then ENTER. End Set END mode Arrow back to PV, then choose SOLVE on the menu ([F] on the HP 48G series or [F6] on HP 49G). 103,388.26 Solve for amount to borrow CANCEL, then ON Registers are displayed Exit the TVM input form 14000, then [+] 117,388.26 Add down payment to get maximum purchase price.
TVM tips
Following are some tips to use when solving TVM problems, to help arrive at the correct answer:
• Set the appropriate payment mode. (Mortgages and loans are typically END mode calculations, and leases are typically BEGIN mode calculations).
• Specify the correct number of payments per year (P/YR).
• Be sure the correct interest rate is entered.
• The compounding period must be the same as the payment period. (If not, interest rate conversion functions will need to be used to calculate the correct rate).
• Remember the sign convention: money received = positive number, money paid out = negative number.

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