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Hi there, if you are following the example from page 24 of the manual - The steps are as follows - reset or clear the previous values by pressing the orange key (2nd F) and MODE.
Then make sure that BGN is not displayed (To do this press 2nd F and FV (above it you will see BGN/END)). To set the number of payments per year press 2nd F I/Y (above it is P/Y). Type in 12 and press ENT. Press the down arrow key and to make sure C/Y also says 12 (12 compounding periods per year). Then press on. Calculate the total number of payments - to do this type in 20 2nd F N (to get xP/Y) and then store the answer in N by pressing N again. (Your screen should say ANS -> 240.00)Type in your present value 56000 and press PV to store it. Enter the monthly payment press +/- 440 PMT. Enter your future value (press 0 then FV). Now to calculate the interest rate press COMP I/Y. It should give you 7.17 %
A very common error is not pressing N to store the number of total payments into the calculator.
If this is not the example you meant, please let me know - and I will explain the other example.
To calculate present value you need to type in all the other missing values and then press COMP and PV.
For example: if the future value is R5000, the interest is 12% p.a. compounded monthly and it paid over 3 years.
Type in 5000 and press FV
type in 12 and I/Y
Press 2nd F and I/Y and make sure P/Y says 12 (for 12 payments per year).
press 3 press 2nd F N and then press N again (for 36 payments in total). Make sure your screen says ANS -> N otherwise the calculation will not work.
Now if if your payments are 0 (in other words you are not making monthly payments) then press 0 and PMT,
Otherwise, if you are making monthly payments for e.g. R200 a month, type in +/- 200 PMT.
Now calculate your original amount by pressing COMP PV.
If you made no payments your original amount should be -3494.62
And if you chose to add payments your original amount should be
Viola. The initials TVM stand for Time-Value-Money; it's a widely used tool throughout financial mathematics. If you are looking to deal with annuities, bonds, present value equations, future value equations, or even certain stocks then you will want to use the TVM app within your TI-84.
When you go into that menu screen you will see about 10 input lines; and despite how you're being taught you'd be best off using only five (from a mathematical & conceptual standpoint). The backbone of the TVM is the time-zero equation of value. So, all you want to be touching is the N, I/Y, PV, PMT, and FV keys.
Background on TVM: N = Number of intervals I/Y = Effective Interest Rate Per Interval (5% is .05 but the computer wants it entered as 5.0) PV = The Present Value PMT = Recurring Payment (either deposit or withdrawal) FV = Future Value
There are like 3 other inputs that I encourage you to ignore (in exchange for learning exactly what's going on within this application).
NOTE: You MUST make your effective interest term match your number of intervals. For example, an annuity with monthly payments for 5 years with a monthly effective interest rate of 2% would need an N value of 60 (which is 12 months per year times 5 years for a total of 60 months).
There's more that could be said, but I think this should help you find the PV of an annuity.
The present value of any future monthly (?) stream of payments stretching some 24 years into the future takes into account the time value of money and depends on the interest rate assumed to apply for each month throughout those 24 years.
There are formulae to calc this for an equal monthly payment and a constant interest rate, over the term but for a variable interest rate you need a spreadsheet.
In the simple case of zero interest assumed throughout the term, present value = current principal balance, but for any positive interest rate, the total present value of the future payment stream is less than the current principal balance.