BA II Plus Time Value of Money: 5 Keys Explained
BA II Plus time value of money problems come down to five keys: N, I/Y, PV, PMT, and FV. Clear old values with 2ND, then CLR TVM. Enter the four values you know, with cash you pay out as a negative number. Then press CPT and the fifth key to get the answer.
This guide is written for the Texas Instruments BA II Plus. Other financial calculators use the same five ideas, but their keys can differ. If you are an Intermediate Accounting student, your real job is to turn a cash-flow timeline (a simple sketch of when each amount is paid or received) into the right calculator entries. The calculator does the rest. Before you start any problem, check two settings: payments per year (P/Y) and payment timing (END or BGN).
Key takeaways
- The five TVM keys are N (number of periods), I/Y (annual interest rate), PV (present value), PMT (payment), and FV (future value).
- Enter any four values, then press CPT and the fifth key to solve for it.
- Cash you pay out is negative. Cash you receive is positive. If every amount has the same sign, you get Error 5 when you solve for the rate or the number of periods.
- 2ND, then FV (CLR TVM) clears the five keys. It does not reset P/Y, C/Y, or BGN, so check those separately.
- Use END for an ordinary annuity (payments at the end of each period) and BGN for an annuity due (payments at the beginning).
- N is the total number of periods. Monthly payments for three years means N = 36. In the Harbor Design example, one deposit grows for three annual periods, so N = 3 even though PMT = 0.
Watch the financial-calculator example
In this short segment, Professor Farhat prices a 30-year, $1,000 bond that pays 8% annual interest in semiannual installments of $40. Watch how he enters it: N = 60 and I = 4. He divides the 8% annual rate by 2 himself, which works when P/Y is set to 1. The section on monthly and semiannual periods below shows how that lines up with the method used in this guide.
Watch this segment on YouTube (9:41–11:28). The video enters the rate per period (4). The written examples in this guide enter the annual rate and let P/Y do the dividing. Both give the same answer, as long as you never mix the two.
What do the five TVM keys on the BA II Plus mean?
Time value of money (TVM) is the idea that a dollar today is worth more than a dollar received later, because today’s dollar can earn interest. TVM math connects cash flows that happen on different dates. Present value brings later cash back to today; future value carries cash forward. The calculator performs the arithmetic after you identify the timing. If the idea itself is new to you, start with time value of money in accounting.
| Key | Meaning | What to enter |
|---|---|---|
| N | Number of payment or compounding periods | Total periods, not automatically years |
| I/Y | Nominal annual interest rate | The stated yearly rate, before compounding. Enter 5 for 5%, not 0.05. P/Y and C/Y convert it to a rate per period |
| PV | Present value | Cash amount at the starting date |
| PMT | Payment | Equal recurring cash flow; zero for a single sum |
| FV | Future value | Cash amount at the final date |
Here is the sign rule: cash you pay out is negative, and cash you receive is positive. Pick one point of view, the investor’s or the borrower’s, and keep it for the whole problem. For example, a deposit leaves the investor’s pocket, so it is negative. A later withdrawal comes back, so it is positive. If PV, PMT, and FV all carry the same sign, the calculator cannot solve for the rate or the number of periods, and it shows Error 5. Texas Instruments explains the TVM variables and annual-rate convention.
Match the five BA II Plus TVM keys
Before entering a cash flow, identify which BA II Plus key represents it. Match N, I/Y, PV, PMT, and FV to their meanings.
How do you set up the BA II Plus for a TVM problem?
- Clear the TVM values. Press 2ND, then FV (CLR TVM). This clears N, I/Y, PV, PMT, and FV. It does not touch P/Y, C/Y, or END/BGN, so check those in the next two steps.
- Set P/Y and C/Y. Press 2ND, then I/Y to open P/Y. Enter the payments per year and press ENTER. Press the down arrow to inspect C/Y, enter the compounding periods per year, and press ENTER. Press 2ND, then CPT (QUIT).
- Check END/BGN. Press 2ND, then PMT to inspect payment timing. Press 2ND, then ENTER (SET) only if the displayed mode needs changing. Press 2ND, then CPT to quit.
Use P/Y = 1 and C/Y = 1 for every annual example below. Do not assume the default. A Texas Instruments support article says a reset sets P/Y to 12 on the BA II Plus and to 1 on the BA II Plus Professional, while its online guidebook lists a default of 1. Earlier work can also leave a different setting behind, so always look before you start. The Texas Instruments settings instructions explain these controls.
Three quick setup tips:
- When you enter a new P/Y, the calculator sets C/Y to the same value automatically. Change C/Y only when interest compounds on a different schedule than the payments.
- To check what is stored in a key, press RCL and then the key. For example, press RCL, then N.
- For a clean slate, press 2ND, then +/− (RESET), then ENTER. This clears everything and restores the factory settings, so recheck P/Y afterward.
Exam tip: build a three-step habit before every problem. Clear TVM, look for BGN on the display, and confirm P/Y. It takes five seconds and heads off the most common mistakes.
What if payments are monthly or semiannual?
Many problems do not use annual periods. Bonds usually pay interest twice a year, and loans are usually paid monthly. You can handle this in two ways. Both are correct. Mixing them is the mistake.
The examples in the table use a nominal annual rate with compounding at the same frequency as the payments. When those frequencies differ, enter the annual rate in I/Y and set P/Y and C/Y to their actual frequencies so the calculator converts the rate correctly.
| Method 1: rate per period | Method 2: annual rate | |
|---|---|---|
| P/Y and C/Y | Leave both at 1 | Set both to the number of payments per year |
| I/Y | Divide the annual rate yourself | Enter the annual rate |
| N | Total number of periods | Total number of periods |
| 6% a year, monthly payments, 3 years | I/Y = 0.5 and N = 36 | P/Y = C/Y = 12, I/Y = 6, and N = 36 |
| 8% a year, semiannual payments, 30 years | I/Y = 4 and N = 60 | P/Y = C/Y = 2, I/Y = 8, and N = 60 |
Method 1 is the one used in the video above. It works the same way present value tables do, with a number of periods and a rate per period. Method 2 is the one built into the BA II Plus.
Here is the bond from the video, done both ways. It pays $40 every six months for 30 years, returns $1,000 at the end, and is priced at an 8% market rate. With either set of inputs, PMT = 40 and FV = 1000 give PV = −1,000.00.
Now mix the two methods. Set P/Y = 2 and also enter I/Y = 4. The calculator divides the 4 a second time and returns −1,695.22. Nothing on the display warns you, so pick one method and stay with it.
In both methods, N is the total number of periods. For a payment stream, this equals the number of payments. A shortcut for Method 2: type the number of years, press 2ND, then N (xP/Y), and the calculator multiplies by P/Y for you. Then press N to store the result. For more on rates per period, see compounding periods explained.
How do you find the future or present value of a single sum?
Hypothetical example. Harbor Design invests $8,000 for three years at 6% compounded annually, with no additional deposits. Confirm annual settings and clear TVM first.
| Action | Entry | Reason |
|---|---|---|
| Set periods | 3 → N | Three annual periods |
| Set rate | 6 → I/Y | 6% per year |
| Enter the investment | 8000 → +/− → PV | An $8,000 cash outflow |
| Remove recurring payments | 0 → PMT | Only one initial deposit |
| Compute future value | CPT → FV | Result: $9,528.13 |
The check is $8,000 × 1.063 = $9,528.128. The display rounds the result to cents; the calculation uses greater precision. For the formula behind this answer, see future value of a single sum.
To reverse the question, clear TVM, enter N = 3, I/Y = 6, PMT = 0, and FV = 9528.128. Press CPT, then PV. The result is −$8,000, the investment required today. Review present value of a single sum for the underlying formula.
How do you solve for the interest rate or the number of periods?
Hypothetical example. An investment grows from $10,000 to $12,100 in two years without other payments. With annual settings, enter N = 2, PV = −10000, PMT = 0, and FV = 12100. Press CPT, then I/Y. The answer is 10%.
If the rate is known instead, enter I/Y = 10 and the same cash flows, then compute N. The result is 2 periods, or two years here. Clear and re-enter the known variables when changing questions so a previously computed number is not mistaken for a new input. For more practice, work through these single-sum problems.
How do you solve for a loan payment (PMT)?
Hypothetical example. You borrow $20,000 for a car at a 6% annual rate and repay it with 48 equal month-end payments. Because the payments are monthly, set P/Y = 12 first (C/Y follows automatically) and confirm END. Then clear TVM.
| Action | Entry | Reason |
|---|---|---|
| Set periods | 48 → N | 48 monthly payments |
| Set rate | 6 → I/Y | 6% a year; P/Y = 12 turns it into 0.5% a month |
| Enter the loan | 20000 → PV | Cash you receive today, so it is positive |
| Nothing owed at the end | 0 → FV | The loan is fully paid off |
| Compute the payment | CPT → PMT | Result: −$469.70 |
The answer is negative because each payment is cash you pay out. If you would rather keep P/Y = 1, enter I/Y = 0.5 and N = 48 instead. You get the same −$469.70.
You can check the loan payment in Excel with =PMT(6%/12,48,20000). The result is −$469.70, matching the BA II Plus.
When you finish, set P/Y back to 1 before you return to the annual examples. For more payment problems, see present value annuity problems.
When do you use END and when do you use BGN?
An annuity is a series of equal payments at equal intervals. END places payments at each period’s end. BGN places them at each period’s beginning. BGN is displayed when active; ordinary END operation has no BGN indicator.
This timeline shows when the three deposits in the next example happen under each setting.
| Setting | Today | End of Year 1 | End of Year 2 | End of Year 3 |
|---|---|---|---|---|
| END (ordinary annuity) | No deposit | $1,500 | $1,500 | $1,500 |
| BGN (annuity due) | $1,500 | $1,500 | $1,500 | No deposit |
Hypothetical example. Deposit $1,500 annually for three years at 6%, starting with no balance. Enter N = 3, I/Y = 6, PV = 0, and PMT = −1500.
| Timing | Setting | Computed FV at Year 3 |
|---|---|---|
| Deposits at ends of Years 1–3 | END | $4,775.40 |
| Deposits at beginnings of Years 1–3 | BGN | $5,061.92 |
Changing timing gives each deposit an extra year of interest: $4,775.40 × 1.06 = $5,061.92, rounded. The number of deposits remains three.
For three $1,500 receipts, enter PMT = +1500 and FV = 0, then compute PV. END gives −$4,009.52; BGN gives −$4,250.09. In plain terms, you would pay $4,009.52 today for three year-end receipts of $1,500, or $4,250.09 if the first receipt comes today. Restore END afterward when the next problem uses year-end payments. To see the formulas behind these answers, read future value of an ordinary annuity, present value of an ordinary annuity, and present value of an annuity due.
How do you price a bond on the BA II Plus?
Hypothetical example. A three-year bond has a $10,000 face amount, a 4% stated rate, annual year-end interest, and a 5% market rate. The stated rate (also called the coupon rate) sets the cash interest the bond pays: $10,000 × 4% = $400 a year. The market rate is the return investors require today, and it is the rate you enter in I/Y.
Use END, P/Y = C/Y = 1, N = 3, I/Y = 5, PMT = +400, and FV = +10000. Press CPT, then PV: −$9,727.68. The price is $9,727.68. Interest and principal are both inflows to the investor, so they have the same sign.
The market rate discounts both cash-flow components. The stated rate determines PMT. This is a combined present-value calculation; the bond pricing lesson explains why the price is below face amount.
Most bonds pay interest twice a year, so try the same bond with semiannual interest. Keep P/Y = 1 and convert everything to six-month periods: N = 6 (3 years × 2), I/Y = 2.5 (5% ÷ 2), PMT = +200 ($10,000 × 4% ÷ 2), and FV = +10000. Press CPT, then PV: −$9,724.59. The price is $9,724.59, a little lower than the $9,727.68 you got with annual interest.
The common trap is changing only one input. If you double N, you must also halve the rate and the payment.
Compare financial-calculator and Excel inputs
| Issue | BA II Plus | Excel |
|---|---|---|
| 6% annual interest, annual periods | I/Y = 6; P/Y = C/Y = 1 | rate = 6% |
| 6% nominal annual interest, monthly periods | I/Y = 6; P/Y = C/Y = 12 | rate = 6%/12 |
| Beginning payments | BGN | type = 1 |
| End payments | END | type = 0 |
| Choose the unknown | CPT, then its key | Select PV, FV, PMT, RATE, or NPER |
Use the companion time value of money in Excel guide to check your results in a spreadsheet. Both methods should agree when the cash flows and settings agree.
Why is my BA II Plus giving the wrong answer?
When an answer looks wrong, the calculator is almost never broken. Check five things before you repeat the calculation: old TVM values, P/Y and C/Y, payment timing, signs, and how you typed the rate. The table shows what each mistake does to the examples in this guide, so you can spot the pattern.
| What you see | Likely cause | Fix |
|---|---|---|
| Error 5 when you compute I/Y or N | PV, PMT, and FV all have the same sign | Press CE/C, enter the cash you paid as a negative number, and compute again |
| $14,303.53 instead of $9,528.13 in the Harbor Design example | A PMT of −1,500 was still stored from an annuity problem | Enter 0 → PMT, then CPT → FV. If you use 2ND, then FV (CLR TVM), re-enter N = 3, I/Y = 6, PV = −8000, and PMT = 0 before pressing CPT → FV. |
| $8,120.60 instead of $9,528.13 in the Harbor Design example | P/Y was still 12, so 6% was treated as 0.5% per period | Set P/Y and C/Y back to 1 |
| $8,014.41 instead of $9,528.13 in the Harbor Design example | You typed 0.06 in I/Y, which means 0.06%, not 6% | Enter 6 → I/Y |
| −$9,782.14 instead of −$9,727.68 for the bond | BGN was still on from an annuity due problem | Press 2ND, then PMT, then 2ND, then ENTER (SET) so END shows. Press 2ND, then CPT (QUIT) |
Texas Instruments lists four of these checks (old values, P/Y and C/Y, signs, and payment timing) in its own troubleshooting guide. Small differences from printed tables usually come from rounded table factors. Large differences mean an input or a setting is wrong.
Five practice questions with answers
All scenarios are hypothetical. Use annual settings unless stated otherwise and round final dollar amounts to cents.
1. Compute future value
What will a $2,500 deposit become after two years at 8% annually?
Answer and explanation
N = 2, I/Y = 8, PV = −2500, PMT = 0; CPT FV gives $2,916.00. The deposit and ending balance have opposite signs.
2. Identify the timing
Four equal deposits occur today and at the beginnings of the next three years. Which mode and N apply?
Answer and explanation
BGN and N = 4. There are four beginning-of-period deposits. Do not reduce N merely because the first payment is today.
3. Fix the monthly setup
A student enters I/Y = 0.5, P/Y = 12, and C/Y = 12 for a 6% nominal annual rate compounded monthly. What should change?
Answer and explanation
Enter I/Y = 6. P/Y and C/Y already convert the annual rate. Entering 0.5 divides the rate a second time.
4. Solve for the payment
A company borrows $20,000 and repays it with four equal year-end payments at 6%. How much is each payment?
Answer and explanation
N = 4, I/Y = 6, PV = 20000, FV = 0; CPT PMT gives −$5,771.83. The payment is negative because it is cash paid out.
5. Diagnose the error
You enter N = 2, PV = 10000, PMT = 0, and FV = 12100, then press CPT and I/Y. The display shows Error 5. What went wrong?
Answer and explanation
PV and FV have the same sign, so the calculator sees no cash going out. Enter PV = −10000 and compute again. The answer is 10%.
Ready to keep going? Try the Farhat Lectures free sample course, or explore the full Intermediate Accounting course.
Frequently asked questions
Does CLR TVM reset payment frequency and BGN?
No. CLR TVM (2ND, then FV) clears only the five TVM values: N, I/Y, PV, PMT, and FV. P/Y, C/Y, and the END/BGN setting stay exactly as they were, so check them separately before you start.
Is a negative PV answer wrong?
No. With positive future receipts, negative PV represents the equivalent investment today. Report the positive magnitude when describing the price.
Can I follow these exact keys on another calculator?
The five-variable logic transfers, but key labels, rate conventions, and settings can differ. Consult that model’s manual.
Why does my BA II Plus show Error 5?
Error 5 means the calculator found no solution. In a TVM problem, the usual cause is that PV, PMT, and FV all have the same sign, so the calculator sees cash moving in only one direction. Press CE/C, enter the cash you paid as a negative number, and compute again.
Should P/Y be 1 or 12 on the BA II Plus?
Either setting works if you stay consistent. With P/Y = 1, you divide the annual rate yourself and enter the rate per period. With P/Y = 12, you enter the annual rate and the calculator divides it for you. Wrong answers come from doing both at once.
How do I change the number of decimal places on the BA II Plus?
Press 2ND, then the decimal point key (FORMAT). Type the number of decimal places you want, such as 4, and press ENTER. Then press 2ND, then CPT (QUIT). This changes only what the display shows. The calculator still computes with more digits than it shows.
Can I use the BA II Plus on the U.S. CPA Exam or CMA exam?
For the U.S. CPA Exam, personal calculators are prohibited in the testing room, and the exam software provides an on-screen calculator and a spreadsheet. IMA’s CMA calculator policy permits the Texas Instruments BA II Plus. Check the NASBA CPA Exam Candidate Guide and the IMA CMA Handbook for the current rules before exam day.
About the author: This guide was written by Mansour Farhat, CPA, CIA, DBA, the instructor behind Farhat Lectures. Learn more about Professor Farhat.
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