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HP 10B and 10BII 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 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, 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
The TVM capability in the HP calculators 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 (See 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.

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:
 Keystrokes Display Notes Shift, then CLEAR All on the 10B or Shift, C All on the 10BII 0.00 Clear registers If BEGIN shows in the display, press shift, BEG/END (BEGIN will not be displayed) Set END mode 25, shift, then XP/YR 300.00 Number of payments 8.75, then I/YR 8.75 Annual interest rate 850, [+/-], then PMT -850.00 Monthly payment 0, then FV 0.00 Future value = 0 (i.e. mortgage paid out) PV 103,388.26 Calculate amount to borrow [+], 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:
• Clear all 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.)
• Specify the correct number of payments per year ( [P/YR] ). For example, 12 shift [P/YR] sets 12 payments per year. Pressing SHIFT and then holding the CLEAR ALL or C ALL button will display the payments per year setting.
• 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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