```html

TI-89 Financial Functions: A Quick Start Guide

The TI-89 calculator, while primarily known for its advanced algebra capabilities, also packs a powerful suite of financial functions. This tutorial provides a concise overview of how to use these functions for common financial calculations.

Accessing the Finance Application

First, you need to access the finance application. Press APPS, then select Finance... (usually option 1). Inside the Finance menu, you'll find several sub-applications, including "TVM Solver," "Amortization," and others. We'll focus primarily on the TVM (Time Value of Money) Solver.

The TVM Solver: Core Concepts

The TVM Solver is the workhorse of the TI-89's financial functions. It allows you to calculate various parameters related to loans, investments, and annuities. The key variables are:

• N: Total number of compounding periods. (e.g., for a 30-year mortgage with monthly payments, N = 30 * 12 = 360)
• I%: Annual interest rate (as a percentage, not a decimal). Enter 5 for 5%, not 0.05.
• PV: Present Value. This is the initial value of the loan or investment. Usually positive if you're receiving money (loan), and negative if you're investing.
• PMT: Payment amount per period. Typically negative for payments you make, and positive for payments you receive.
• FV: Future Value. This is the value of the investment or loan at the end of the period. Often 0 for loans.
• P/Y: Payments per year. Usually 12 for monthly payments, 1 for annual payments.
• C/Y: Compounding periods per year. Often the same as P/Y, but can differ (e.g., a loan with monthly payments but annual compounding).
• PMT: BEGIN END: Specifies whether payments are made at the beginning or end of the period. Select the appropriate option using the arrow keys and press ENTER. Most loans are "END" (ordinary annuity).

Calculating with the TVM Solver

1. Navigate to the TVM Solver within the Finance application.
2. Enter values for all but one variable.
3. Place the cursor on the variable you want to calculate.
4. Press ALPHA then SOLVE (the ENTER key). The calculator will solve for the unknown variable.

Example: Calculating Monthly Mortgage Payments

Suppose you want to borrow $200,000 (PV = 200000) at an annual interest rate of 4.5% (I% = 4.5) for 30 years (N = 360). You want to find the monthly payment (PMT). The future value is 0 (FV = 0), P/Y = 12, and C/Y = 12, and PMT is set to END.

Enter the known values into the TVM Solver, place the cursor on PMT, and press ALPHA then SOLVE. The calculator will display the monthly payment (PMT), which will be a negative value because it's a payment you're making.

Important Considerations

• Sign Convention: Be consistent with the sign convention (positive for money received, negative for money paid out).
• Clearing Variables: Before each calculation, it's a good practice to clear the variables in the TVM Solver by setting them to zero or blank.
• Error Messages: If you get an error message, double-check your inputs, especially the interest rate and the number of periods.

The TI-89's finance functions are powerful tools for analyzing financial scenarios. By understanding the TVM Solver and its variables, you can easily calculate loan payments, investment returns, and other financial metrics.

```