HP 50g Calculator - Time Value of Money (TVM) Calculation

Introduction to financial terminology used in solving financial problems

Many financial problems are based on the concept of charging a fee (interest) for the use of someone else's money over a fixed period of time. The phrase, time value of money (TVM) describes these types of financial calculations.

In TVM calculations, the most common problems use two types of interest:

  • Compound interest

  • Simple interest

With simple interest, only the principal (the original amount of money) earns interest for the entire duration 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 examples of compounded interest calculations.

TVM elements

The standard variables used to describe most compound interest (TVM) problems:

TVM Element
Description
n
Number of payments
I%YR
Annual interest rate
P/YR
Number of periods per year
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 ‘Solve finance’ option of the Numerical Solver (NUM.SLV) menu is used for these types of TVM calculations. To access the 'TIME VALUE OF MONEY' input page, press . This application can also be started by using the keystroke combination .
To solve an unknown variable, use the arrow cursor keys to move about the page and key in all known values in the highlighted fields. Once all known variables have been assigned values, highlight the field of the unknown value with the cursor keys, and press the key to calculate it.

TVM example

Calculating the payment on a loan

If $2 million is borrowed at an annual interest rate of 6.5% to be repaid in 60 monthly payments, what should be the monthly payment? For the debt to be totally repaid in 60 months, assume the future value of the loan will be zero, and payments will be made at the end of each compounding period. For this example, use the following values: n = 60, I%YR = 6.5, PV = 2000000, FV = 0, P/YR = 12. To enter the data and solve for the payment, PMT:

Key
Description
Start the financial calculation input form.
Enter 'n' = 60
Enter 'I%YR' = 6.5 %
Enter 'PV' = 2,000,000 US$
Skip 'PMT', since we will be solving for it
Enter 'FV' = 0, the option 'End' is highlighted
Use the cursor keys to highlight the 'PMT' field.
NOTE: A new option appears in the menu, 'SOLVE'.
Press the soft menu key to find the payment.

The solution screen appears as shown below:

Figure 1: The solution screen
NOTE: The final solution is a negative value. Although it may seem odd, the answer is correct, because the calculator solves TVM problems based on cash flow diagrams. Cash flow diagrams identify both positive and negative cash flows in financial problems. In this case, the loan is considered a positive cash flow; it is the money received. The payment is a negative cash flow, and, as such, it has a negative value. It is the money payable.