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HP 17Bii, 17Bii+, and 19Bii 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 phrasetime value of money (TVM) describes the calculations based on such problems.
There are two main types of financial problems:
  • 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, 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
Total number of periods
I
Annual interest rate
PV
Present value
PMT
Payment amount each period (periodic payment amount)
FV
Future value
Given any four of the above variables, it is possible to solve for the fifth variable.
The TVM capability does many compound-interest problems. The TVM functionality can be used for a series of cash flows (money paid, or money received) when:
  • The dollar amount is the same in each payment.
  • The payments occur at regular intervals.
  • The payment period coincides with the compounding periods.
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. (See Figure 1.) It is essential to use the correct sign (positive or negative) for TVM numbers. 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.
TVM example
The monthly mortgage repayment you can make is $850. You have $14,000 as 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 this example problem:
  note:
All italicized keys are soft menu keys located on the bottom of the screen. Access these by the top row of keys on the keypad.
Keystrokes
Display
Notes
Press the Orange shift key, then CLEAR DATA
(the display is not changed)
Clear the financial registers.
Press FIN
SELECT A MENU
Select the Financial Menu.
Press TVM, then OTHER
# PMTS/YR: BEGIN (or END) MODE
Select the TVM Menu and choose the other option.
Type 12 then press P/YR, then END
12 P/YR END MODE
Select 12 periods per year and place the compounding mode to end.
Press the EXIT key
12 P/YR END MODE
Exit to the main TVM menu choices.
Type 25, press the orange shift key, then N
N=300.00
Enter the number of periods in 25 years.
Type 8.75 then press I%YR
I%YR=8.75
Interest rate
Type 850, then press the +/- key, then PMT
PMT=-850.00
Monthly payment
Type 0, then press FV
FV=0.00
Future value = 0 (mortgage paid off)
Press PV
PV=103,388.26
Amount to finance
Press addition (+) key, type 14000, then press the equal (=) key
117,388.26
Add the down payment to get maximum purchase price.
TVM tips
To assure the answers are correct follow the recommended steps below:
  • Clear the TVM variables before beginning a new calculation. This removes unwanted values from the calculator memory.
  • Set the appropriate payment mode. (Mortgages and loans are typically END mode calculations, and leases are typically BEGIN mode calculations.
  • 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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