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
- 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.
- 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?
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.