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Leasing versus Borrowing with the TI-83 Plus

You can use the TI-83 Plus graphing calculator to determine whether leasing is a better deal than borrowing. Suppose that you’re planning to purchase a $2,000 laptop. Which of the following approaches can give you the better deal?

  • Lease the laptop for $600 a year for four years with the option to buy the laptop after four years for an additional $300.

  • Take out a four-year loan at 12% simple interest.

The internal rate of return is the yearly simple interest rate that you earn on an investment plan. In the context of a lease, the internal rate of return is the yearly simple interest rate you would pay if the lease were converted to a loan. So to find the better deal, you must compare the lease’s internal rate of return to 12% (the loan’s internal rate of return).

To find the lease’s internal rate of return:

  1. Set the second line of the Mode menu to Float.

    When dealing with money, you usually set the second line of the Mode menu to 2 so all numbers are rounded to two decimal places. When you’re comparing interest rates, however, you want to see as many decimal places as possible. You can do so by setting the second line to Float.

  2. Press [APPS][1] to start the Finance application. (On the TI-83, press [2nd][x–1].)

  3. Repeatedly press

    image0.png

    to move the indicator to the irr command and press [ENTER].

  4. Enter the initial cash flow and press [.].

    For the leasing program described, the initial cash flow is the $2,000 price of the laptop.

  5. Enter the cash-flow list and press [.].

    In the leasing-program scenario, the cash flow indicates what you paid per year to lease the laptop: $600 a year for the first three years, and $900 in the fourth year (that is, $600 to lease it and then $300 to purchase it). So the cash-flow list is {-600, -900}. You enter the frequencies for this list in the next step.

    Enter the cash-flow list as a list contained within braces, using commas to separate the elements in the list. You enter the braces into the calculator by pressing [2nd][ ( ] and [2nd][ ) ]. (Remember to use the [(-)] key to indicate that a number is negative.)

  6. Enter the cash-flow frequency list.

    The cash-flow frequency list indicates how frequently each element (in this case, each specific amount) occurs in the cash-flow list. In the leasing-program scenario, the cash-flow frequency list is {3, 1} because $600 was paid for the first three years and $900 was paid in the fourth year.

  7. Press [ ) ][ENTER] to calculate the internal rate of return.

    This procedure is illustrated. This figure also shows the answer to the question posed at the beginning: You’re better off taking out the loan at 12% simple interest because leasing the laptop is equivalent to a 12.29% loan.

    image1.jpg
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