How To Use Financial Calculator Ti 84 Plus

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The TI 84 Plus Calculator

In the previous section nosotros looked at the basic time value of money keys and how to use them to calculate present and future value of lump sums. In this section we will take a await at how to use the TI 84 Plus to calculate the nowadays and future values of regular annuities and annuities due.

A regular annuity is a serial of equal cash flows occurring at equally spaced fourth dimension periods. In a regular annuity, the first cash flow occurs at the stop of the beginning period.

An annuity due is similar to a regular annuity, except that the start greenbacks flow occurs immediately (at period 0).

Example 2 — Present Value of Annuities

Suppose that you are offered an investment that will pay you $1,000 per year for 10 years. If you can earn a rate of ix% per year on like investments, how much should y'all be willing to pay for this annuity?

In this case nosotros demand to solve for the present value of this annuity since that is the corporeality that you would be willing to pay today. Enter the numbers onto the appropriate lines: 10 into N, 9 into I%, grand (cash arrival) into PMT, and 0 for FV. Motion to the PV line and printing Alpha Enter to solve the trouble. The answer is -half dozen,417.6577. Once again, this is negative because it represents the corporeality yous would have to pay (cash outflow) today to purchase this annuity.

Example two.1 — Future Value of Annuities

Now, suppose that y'all will be borrowing $yard each year for 10 years at a rate of 9%, and and then paying dorsum the loan immediate afterwards receiving the concluding payment. How much would y'all have to repay?

All we need to do is to put a 0 into PV to clear information technology out, and then solve for FV to find that the answer is -15,192.92972 (a cash outflow).

Example 2.2 — Solving for the Payment Amount

We often demand to solve for annuity payments. For example, you might want to know how much a mortgage or auto loan payment volition exist. Or, maybe you desire to know how much you will need to relieve each yr in society to accomplish a particular goal (saving for college or retirement perchance). On the previous page, we looked at an example about saving for college. Allow'south look at that problem once more, but this time nosotros'll treat it as an annuity problem instead of a lump sum:

Suppose that yous are planning to send your daughter to college in 18 years. Furthermore, assume that you lot have determined that y'all will demand $100,000 at that fourth dimension in guild to pay for tuition, room and board, political party supplies, etc. If you believe that you can earn an boilerplate annual charge per unit of return of 8% per year, how much money would you need to invest at the finish of each year to achieve your goal?

Recall that we previously adamant that if you were to make a lump sum investment today, you would have to invest $25,024.xc. That is quite a chunk of change. In this example, saving for college volition exist easier because we are going to spread the investment over eighteen years, rather than all at one time. (Annotation that, for at present, we are assuming that the first investment will be made one yr from at present. In other words, it is a regular annuity.)

Let's enter the information: Blazon 18 into N, 8 into I%, and 100,000 into FV. At present, solve for PMT and you will find that you need to invest $ii,670.21 per twelvemonth for the adjacent eighteen years to meet your goal of having $100,000.

Example two.3 — Solving for the Number of Periods

Solving for N answers the question, "How long volition it take..." Allow'south expect at an instance:

Imagine that you have simply retired, and that y'all take a nest egg of $1,000,000. This is the corporeality that you will be cartoon downward for the residuum of your life. If you look to earn 6% per year on average and withdraw $lxx,000 per year, how long volition information technology take to burn through your nest egg (in other words, for how long can you afford to live)? Assume that your first withdrawal volition occur one twelvemonth from today (End Mode).

Enter the data as follows: 6 into I%, -1,000,000 into PV (negative because you are investing this corporeality), and 70,000 into PMT. At present, solve for N and yous will meet that you can make 33.40 withdrawals. Bold that you can live for about a year on the final withdrawal, then y'all can afford to live for about another 34.40 years.

Case 2.iv — Solving for the Interest Rate

Solving for I% works just similar solving for any of the other variables. Every bit has been mentioned numerous times in this tutorial, be sure to pay attention to the signs of the numbers that y'all enter into the TVM keys. Any time y'all are solving for Northward, I%, or PMT there is the potential for a incorrect reply or error message if you don't go the signs right. Permit'due south wait at an example of solving for the interest charge per unit:

Suppose that yous are offered an investment that will cost $925 and volition pay you interest of $80 per twelvemonth for the side by side 20 years. Furthermore, at the stop of the 20 years, the investment will pay $1,000. If yous purchase this investment, what is your compound average annual charge per unit of return?

Annotation that in this problem nosotros have a nowadays value ($925), a futurity value ($1,000), and an annuity payment ($80 per year). As mentioned above, you need to be especially careful to get the signs correct. In this case, both the annuity payment and the future value will be greenbacks inflows, so they should exist entered as positive numbers. The present value is the cost of the investment, a cash outflow, so it should be entered as a negative number. If you were to make a mistake and, say, enter the payment equally a negative number, then y'all volition go the wrong respond. On the other hand, if y'all were to enter all three with the same sign, so you will get an error message,

Permit's enter the numbers: Type 20 into North, -925 into PV, 80 into PMT, and k into FV. Now, solve for I% and y'all will find that the investment will return an average of 8.81% per yr. This particular problem is an example of solving for the yield to maturity (YTM) of a bond.

Example 2.5 — Annuities Due

In the examples in a higher place, nosotros assumed that the first payment would exist made at the end of the year, which is typical. Even so, what if yous plan to make (or receive) the first payment today? This changes the cash flow from from a regular annuity into an annuity due.

Normally, the calculator is working in End Mode. It assumes that cash flows occur at the terminate of the period. In this case, though, the payments occur at the commencement of the menstruation. Therefore, we need to put the computer into Begin Mode. To change to Begin Mode, curlicue down to the bottom of the TVM Solver. You lot should see that Cease is currently highlighted. Now, printing the correct arrow fundamental to highlight Begin, so press ENTER. Note that nothing will change about how y'all enter the numbers. The reckoner will simply shift the cash flows for yous. Plain, you volition get a different answer.

Let's exercise the college savings trouble over again, only this fourth dimension assuming that you start investing immediately:

Suppose that you are planning to send your daughter to higher in 18 years. Furthermore, assume that yous have determined that you will demand $100,000 at that time in society to pay for tuition, room and board, political party supplies, etc. If you believe that you can earn an average annual rate of return of 8% per year, how much money would you need to invest at the beginning of each year (starting today) to achieve your goal?

As earlier, enter the information: 18 into Due north, 8 into I%, and 100,000 into FV. The only thing that has changed is that we are at present treating this every bit an annuity due. And so, once you have inverse to Begin Mode, but solve for PMT. You volition notice that, if you make the starting time investment today, yous only need to invest $2,472.42. That is virtually $200 per yr less than if you make the showtime payment a year from now because of the extra fourth dimension for your investments to compound.

Be certain to switch back to End Mode subsequently solving the problem. Since you virtually always want to exist in End Way, it is a adept idea to arrive the addiction of switching back so that you don't forget. Scroll downward to the bottom of the TVM Solver, highlight Finish and press Enter.

Example 2.six — Perpetuities

Occasionally, we have to deal with annuities that pay forever (at least theoretically) instead of for a finite period of time. This type of cash flow is known as a perpetuity (perpetual annuity, sometimes called an infinite annuity). The problem is that the TI 84 Plus has no mode to specify an infinite number of periods for Due north.

Calculating the nowadays value of a perpetuity using a formula is like shooting fish in a barrel enough: Just divide the payment per period past the interest rate per menstruum. In our instance, the payment is $i,000 per year and the involvement charge per unit is 9% annually. Therefore, if that was a perpetuity, the present value would be:

$11,111.11 = ane,000 ÷ 0.09

If y'all can't remember that formula, you can "play tricks" the figurer into getting the right answer. The play a joke on involves the fact that the present value of a cash catamenia far enough into the futurity (manner into the hereafter) is going to be approximately $0. Therefore, beyond some time to come point in time the cash flows no longer add anything to the nowadays value. So, if we specify a suitably big number of payments, we can get a very close approximation (in the limit information technology will be exact) to a perpetuity.

Let'southward try this with our perpetuity. Enter 500 into N (that will e'er exist a big plenty number of periods), 9 into I%, and 1000 into PMT. At present scroll to PV and printing Alpha Enter and you will get $xi,111.eleven every bit your reply.

Delight note that in that location is no such thing every bit the future value of a perpetuity considering the cash flows never end (menstruum infinity never arrives).

Delight continue on to part III of this tutorial to acquire about uneven cash flow streams, net present value, internal rate of return, and modified internal rate of return.