TVM Solver Introduction

On the TI-83, the right side of this equation should be entered as P*(1 + r / k)^(k*t), with the exponent in parenthesis, so that the multiplication (k*t) is done before the exponentiation, or you'll end up with the wrong answer, namely P*(1 + r / k)^k*t = P*t*(1 + r / k)^k.

Basics of the TVM Solver

You start up the TVM Solver by pressing [2nd][FINANCE][1:TVMSolver] (go ahead and start it now, just to see the menu). A menu should appear that allows you to enter values for several variables. The idea is to enter values for all but one of the variables, and then solve for that variable. In addition, cash outflows (deposits, payments, etc.) are entered as negative numbers. The TVM Solver actually handles much more difficult calculations (mortgages and annuities) than the ones we'll do today, but here is a brief explanation of each of the variables in the TVM Solver.

N = total number of payments (since we don't make payments, we'll set this to the number of years for today);
I% = nominal interest rate, expressed as a percent (use 5, for 5%, NOT 0.05);
PV = present value or principal;
PMT = amount of each payment (for mortgages and annuities, we'll set this to zero today);
FV = future value;
P/Y = payments per year (set this before C/Y, and we'll use 1 payment per year today);
C/Y = compounding periods per year (this is reset to P/Y if you change P/Y);
PMT: END BEGIN to select whether payments are made at end of periods, or beginning. Use END if in doubt.

For today, we won't be using the payment amount variable, so we'll always have PMT = 0 and P/Y = 1 (so N is just the number of years). Similarly (for today), we'll always set our payment time to the end of the period (move your cursor over END in the last line and press [ENTER] to select this). You enter values for the variables by scrolling with the blue arrow keys, and then just typing in the value. Once you've entered values for all but one variable (or all of them), move the cursor to the line containing the variable you'd like to solve for, and press [ALPHA][SOLVE] (the [SOLVE] key is the same as the [ENTER] key, and the [ALPHA] key is green, near the top left of the keypad).
Here are examples to illustrate both algebraic and TVM Solver solutions.

Solving for future value: If you deposit $2500 in an account earning 12% interest compounded weekly, how much is it worth in 4 years?

Algebraically: This is exactly the type of question that our formula is best suited for. We simply enter the given values for each of the variables on the righthand side of the equation, using parenthesis around the exponent. It should look something like the screen below.

The answer is therfore $4037.95
TVM Solver: Start the TVM Solver (press [2nd][FINANCE][ENTER] ). Enter the values shown below. Move the cursor to the future value line, and press [ALPHA][SOLVE]. You should get the same answer as above.

Solving for present value: How much money must you deposit now, if you need $10000 in 4 years, and can earn 5.5% interest compounded monthly?

Algebraically: Start by calculating what you can on the right side of the compound interest formula, namely (1 + 0.055 / 12)^(12*4). To avoid round-off errors, store this value in the variable X. On the TI-83, X is the easiest variable to access; you just press the graphing variable key ([X,T,q,n]). Once you've calculated the value, press [STO>] (just above the [ON] key) X (the graphing variable button) and then press [ENTER] (see the left image below).

Now the variable X should contain the value of (1 + 0.055 / 12)^(12*4), so just enter the value of A (10000) and divide by X. See the right image above. You'd need to deposit $8029.22 to obtain $10000 in 4 years at 5.5% interest compounded monthly.
TVM Solver: Here, we fire up the TVM Solver, set N = 4, I% = 5.5, ignore PV for now, PMT = 0, FV = 10000, P/Y = 1, C/Y = 12. Move to the present value line and press [ALPHA][SOLVE]. The result is negative, since we need to deposit that amount.

Solving for time: How long does it take $5000 at 8% interest compounded daily to reach a value of $7500?

Algebraically: Start by substituting for the variables we know, 7500 = 5000*(1 + .08 / 365)^365t. Since the variable we want (t) is in an exponent, we'll have to use the natural log function to solve for it. For this type of problem, there is a rule of exponents that we can use to simplify things a bit. The rule states that x^a*b = (x^a)^b, and for us, this means that we can get t alone in an exponent. We need to calculate (1 + .08 / 365)³⁶⁵, and when raising any number to that big of a power, we should be extra cautious about round-off error, so we'll store that intermediate result in the variable X again. This is shown (all at once) in the left screen below.

Thus, (with some bad rounding off) our equation is now 7500 = 5000*1.0833^t. We divide through by 5000, to get 1.5 = 1.0833^t. If we take the natural log of both sides, we have ln(1.5) = ln(1.0833^t) = t*ln(1.0833), by a property of logarithms. So we can solve for t by dividing through by ln(1.0833) (actually we'll divide through by ln(X), to avoid round-off error). Now we were lucky this time, in that our value of A / P (7500/5000) was a clean number (1.5), to be safe, we would normally accomplish these last steps by taking ln(A / P), dividing that by ln(X), to obtain our answer (see the middle screen above). It will take 5.07 years (we should round up here to ensure our money is at least $7500) for our money to grow to $7500 in this account.
TVM Solver: We know everything but the amount of time, so enter the values shown on the right screen above (leave N at whatever value it had earlier). Move the cursor to the line for N and press [ALPHA][SOLVE] to get the same answer.