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TI Financial Calculator Functions
TVM Workbook
Underlying formula in familiar form:
[ ] [ ] (^ m^ ) [ ] (1 ) n 0 PV m PMT an FV i
where: m = payments per year i = annual effective interest rate n = number of years of payments (= number of years between date of PV and date of FV )
In the following, assume that the applicable interest rate is i ( k ), where k is the number of interest conversion periods per year.^1 The “ i ” shown in the above formula is the
equivalent annual effective rate:
( ) (1 ) 1
k^ k i i k
Note that [ PV ], [ PMT ], and [ FV ] in the above formula can not all have the same sign. At least one must be positive, and at least one must be negative. (Otherwise the calculated present value could not be 0.)
For Enter N m x n Note: This is always the number of payments. I/Y i ( k )^ x 100 PV [ PV ] PMT [ PMT ] FV [ FV ] P/Y m C/Y k BGN BGN or END (for annuity-due or annuity-immediate, respectively)
After all the known values have been entered (4 out of 5 of N, I/Y, PV, PMT, and FV), press CPT followed by the button for the unknown value.
It is usually advisable to keep P/Y and C/Y both set to 1, and set I/Y equal to the effective interest rate per payment period. This often makes it easier to relate the written formula to the calculator entries. More importantly, it minimizes the likelihood of making an error by forgetting to change the settings for these two values.
(^1) Clarification: The interest rate that we are given may not be the annual effective rate (convertible 1 time
per year). To cover all possible situations, we will assume that the interest rate given in the problem (the rate that we enter as [ I/Y ])is convertible k times per year. If we do know the annual effective rate, then k = 1. Frequently, k equals m (the number of payments per year), but this is not always the case.
TVM Workbook (cont.)
Amortization subprogram within TVM
The Amortization functions should be used after the TVM values have been calculated (i.e., after 4 of the 5 TVM values have been entered and the 5th^ has been calculated using the CPT key). These functions allow you to calculate the outstanding loan balance as of any date during the loan's term, or to determine the amount of principal and interest paid by any loan payment (or by any series of consecutive payments).
Let PV be an initial loan amount that is repaid by N level payments of PMT each, payable P/Y times per year, which are paid at BGN or END of year (depending on the calculator's setting). The loan is subject to an interest rate of I/Y per year (or per whatever period you have decided to use as your “year”), convertible C/Y times per “year.” 2
To use the Amortization function, enter the numbers of the first and last payments for which you want to calculate values:
For Enter P1 the number of the first payment in the range P2 the number of the last payment in the range
For example, if you want to know the amount of interest paid during the second year of a loan with monthly payments, enter 13 for P1 and 24 for P2. Note that P1 will equal P2 if you are calculating the values for just one payment.
Then use the down arrow to see:
BAL = outstanding loan balance after payment number P2 (the 24th^ payment, in this example) PRN = the amount of loan principal that was repaid by payments P1 through P INT = the amount of loan interest that was paid by payments P1 through P2 (which equals the amount of interest accruing on the loan during payments period P1 through P2)
Formulas:
( ) 2
( ) ( ) 1 1 2
( ) 2 1
1 1
m N P m
m m N P^ NP m m m P
t P
BAL LB P LP a
PRN LB P LB P LP a a
i INT LP P P PRN LB t m
−
− − − −
= −
(^2) Note: The value of FV does not affect the AMORT calculations. Typically, FV will be 0, indicating that
the loan is completely repaid after N payments. But if we have entered (or computed) a value of FV greater than 0, this means that the payment amount, PMT, will leave an outstanding balance equal to FV after N payments have been made.
CF Workbook (cont.)
IRR Functions
After the cash flows have been entered, press IRR, then CPT to find the internal rate of return (= interest rate per period at which the present value of the cash flows will be 0).
Also available in IRR functions (BA-II Plus Professional only) by pressing down arrow: RI (an amount the user enters) = reinvestment rate (interest rate earned on funds paid to the investor prior to the final date (i.e., positive cash flows before the date when t = r )) MOD (press CPT to calculate it) = modified internal rate of return (the internal rate of return, including the effect of reinvesting funds at rate RI), calculated as follows:
Let: AV = value of all positive cash flows, accumulated at rate RI to the date of the last cash flow IV = total amount of all negative cash flows added together (without adjustment for interest)
1 1
AV^ r MOD IV
In short, the calculator treats all negative entries (amounts invested) as if they had been invested at time t = 0. (Basically, it assumes that the investor had these funds on hand at time 0 and did not earn any interest on them between t = 0 and the time when they were actually invested.) The interest rate that is calculated is simply the rate at which this total investment amount, if invested at time 0, would have grown to equal the accumulated outflows (positive cash flows, plus interest at rate RI) as of the date of the final cash flow.
NPV Functions
Once all the cash flows have been entered, press NPV.
For Enter I effective interest rate per period^3 (x 100)
For NPV or NFV (net present value or net future value), select that function using the up and down arrows, then press CPT to calculate its value according to the above formulas (shown at the top of the preceding page). Note: NFV is available on the BA-II Plus Professional only.
(^3) For example, if the period (between cash flows) is monthly and the nominal interest rate, i (12), is 9%
(0.09), then calculate [ i (12)^ / 12] x 100 = 0.75and enter 0.75 for I. If the period between cash flows is one month and the annual effective rate is i , then calculate [(1 + i )1/12^ – 1] x 100 and enter that value as I.
ICONV Function
Underlying formula (in three equivalent forms):
( ) 1/
( )
1 ( )
[(1 ) 1]
k k
k k
k k
i k i
i i k i i k
where: i = annual effective rate k = number of interest conversion periods per year i ( k )^ = nominal rate convertible k times per year
For Enter EFF effective interest rate x 100 (if known) NOM nominal interest rate x 100 (if known) C/Y number of interest conversion periods per year ( k )
Then: Use up or down arrows to go to the unknown interest rate (either EFF or NOM). Press CPT to calculate its value.
