Pietro MeloniPhD

IB Calculator Guide / TVM and finance solver

GDC skill · TVM solver · finance solver

TVM solver on your calculator: compound interest, loans and savings for IB Maths AI

IB Maths AI SL and HL (Topic 1, Number and algebra: financial applications). Paper 1 and 2, nearly every session. Not in the AA syllabus.

The AI syllabus says "use of technology" for compound interest, annuities and amortisation, which means the TVM (time value of money) solver. It is one screen with seven fields: number of periods NN, annual interest rate I%I\%, present value PVPV, payment PMTPMT, future value FVFV, payments per year P/YP/Y and compounding periods per year C/YC/Y. You fill in six and solve for the seventh. The only hard idea is the sign convention: money you pay out is negative, money you receive is positive. Students lose marks by mixing the signs (the solver then returns an error or a nonsense rate) and by forgetting that NN counts periods, not years.

The example used below

Maria takes a loan of 12 000 EUR at 4.8% per year, compounded monthly, to be repaid with equal monthly payments over 5 years. (a) Find the monthly payment. (b) Find the total interest paid. (c) Elena instead saves 250 EUR at the end of each month at 3.6% per year compounded monthly. Find how much she has after 8 years.

Answers

(a) 225.36 EUR per month. (b) 60×225.357−12000=1521.4160 \times 225.357 - 12000 = 1521.41 EUR (1520 EUR to 3 s.f.). (c) 27 765.20 EUR (27 800 to 3 s.f.).

Choose your calculator

The page remembers your choice on the other guides.

TI-Nspire CX II

In one line. Calculator page: menu, 8 Finance, 1 Finance Solver. Fill six fields, put the cursor on the seventh and press enter.

  1. 1

    Open a Calculator page and the Finance Solver.

    menu8: Finance1: Finance Solver
  2. 2

    For the loan: N = 60 (5 years × 12), I(%) = 4.8, PV = 12000 (she receives the money, positive), Pmt = 0 for now, FV = 0 (the loan is fully repaid), PpY = 12, CpY = 12, PmtAt = END.

    N: 60I(%): 4.8PV: 12000FV: 0PpY: 12CpY: 12PmtAt: END
  3. 3

    Move the cursor to Pmt and press enter. Pmt = −225.3569. She pays 225.36 EUR a month; the minus sign means money out.

    cursor on Pmtenter
  4. 4

    Total interest: 60 × 225.3569 − 12000 = 1521.41 EUR, done on the Calculator page with the unrounded payment.

  5. 5

    For the savings plan: N = 96, I(%) = 3.6, PV = 0, Pmt = −250 (she pays in), PpY = 12, CpY = 12. Cursor on FV, enter: FV = 27765.20.

    N: 96I(%): 3.6PV: 0Pmt: −250PpY: 12CpY: 12cursor on FVenter

Typed form

  • tvmPmt(N, I, PV, FV, PpY, CpY) tvmFV(N, I, PV, Pmt, PpY, CpY)
  • tvmN, tvmI, tvmPV also exist; all are under menu, 8 Finance, 2 TVM Functions

Where the TI-Nspire CX II trips people up

  • PpY and CpY are kept from the previous problem. Check them every time: a leftover PpY = 1 with monthly payments is a classic.
  • If every value has the same sign the solver cannot find a rate and shows an error: at least one cash flow must be opposite in sign.
  • The tvm functions (tvmPmt etc.) give the same answers in one line and are faster once you know the argument order.

Casio fx-CG50

In one line. MENU, Financial, F2 Compound Interest. Fill the fields, then press the F key of the one you want (F1 n, F2 I%, F3 PV, F4 PMT, F5 FV).

  1. 1

    Open Financial and choose Compound Interest.

    MENUFinancialF2 Compound Interest
  2. 2

    For the loan: n = 60, I% = 4.8, PV = 12000, PMT = 0, FV = 0, P/Y = 12, C/Y = 12. EXE after each value.

    n: 60I%: 4.8PV: 12000FV: 0P/Y: 12C/Y: 12
  3. 3

    Press F4 PMT to solve for the payment: PMT = −225.3569. She pays 225.36 EUR a month.

    F4 PMT
  4. 4

    Press F1 REPEAT to go back to the fields. Total interest = 60 × 225.3569 − 12000 = 1521.41 EUR in Run-Matrix.

    F1 REPEAT
  5. 5

    For the savings plan: n = 96, I% = 3.6, PV = 0, PMT = −250, P/Y = 12, C/Y = 12. Press F5 FV: FV = 27765.20.

    n: 96I%: 3.6PV: 0PMT: −250P/Y: 12C/Y: 12F5 FV

Typed form

  • Payment timing (end or beginning of period) is in SET UP (SHIFT MENU) inside Financial: Payment: End for IB questions unless told otherwise
  • F4 Amortization in the Financial menu gives the interest and principal in a given payment

Where the Casio fx-CG50 trips people up

  • The fx-CG50 asks for the Payment timing in SET UP, not on the screen. End is the default and the IB standard.
  • Casio also has F1 Simple Interest: do not use it for compound questions.
  • The screen keeps the previous values. Set FV to 0 explicitly for a fully repaid loan.

TI-84 Plus CE

In one line. APPS, 1 Finance, 1 TVM Solver. Fill six fields, move to the seventh, press ALPHA ENTER (SOLVE).

  1. 1

    Open the TVM Solver.

    APPS1: Finance1: TVM Solver
  2. 2

    For the loan: N = 60, I% = 4.8, PV = 12000, PMT = 0, FV = 0, P/Y = 12, C/Y = 12, PMT: END highlighted.

    N: 60I%: 4.8PV: 12000FV: 0P/Y: 12C/Y: 12PMT: END
  3. 3

    Move the cursor to PMT and press ALPHA then ENTER (SOLVE). PMT = −225.3569. She pays 225.36 EUR a month.

    cursor on PMTALPHAENTER (SOLVE)
  4. 4

    Total interest: 2nd MODE (QUIT) to the home screen, then 60 × 225.3569 − 12000 = 1521.41 EUR.

  5. 5

    For the savings plan: N = 96, I% = 3.6, PV = 0, PMT = −250, P/Y = 12, C/Y = 12. Cursor on FV, ALPHA ENTER: FV = 27765.20.

    N: 96I%: 3.6PV: 0PMT: −250P/Y: 12C/Y: 12cursor on FVALPHAENTER (SOLVE)

Typed form

  • Home screen: APPS, Finance, then 2 tvm_Pmt, 3 tvm_I%, 4 tvm_PV, 5 tvm_N, 6 tvm_FV use the values stored in the solver
  • Typing P/Y sets C/Y to the same value automatically; change C/Y afterwards if they differ

Where the TI-84 Plus CE trips people up

  • SOLVE is ALPHA then ENTER, not ENTER alone. ENTER alone just moves to the next line.
  • Negative numbers use the (−) key next to ENTER, not the subtraction key.
  • A black square at the left of a field marks the one that was last solved for. Make sure it is the one you wanted.

Where the marks go, on any calculator

  • Sign convention. Loan received: PV positive, payments negative. Savings: payments negative, FV positive. Mixing the signs gives an error or a rate of several hundred per cent.
  • NN in years instead of periods. Five years of monthly payments is N=60N = 60. Match NN to P/YP/Y.
  • Nominal rate confusion. The I% field is the annual nominal rate (4.8), not the rate per month (0.4) and not 0.048.
  • Rounding the payment before computing the total interest. Use the stored full value, round at the end.
  • Using the TVM solver when the question asks for the compound interest formula by hand (AI Paper 1 sometimes does). Then write FV=PV(1+r100k)knFV = PV\left(1 + \tfrac{r}{100k}\right)^{kn} and substitute.

What to write on the paper

  1. List the inputs with their signs: "N = 60, I% = 4.8, PV = 12000, FV = 0, P/Y = C/Y = 12". The mark scheme awards M1 for a correct set of TVM entries.
  2. Give the output with its unit and two decimal places for money unless told otherwise: PMT = 225.36 EUR.
  3. For "total interest" show the arithmetic: 60×225.357−12000=1521.4160 \times 225.357 - 12000 = 1521.41.
  4. If the question gives a real-life rate and asks for a comment, mention inflation or the real rate only if asked: stick to the figures.

Questions students ask

Which sign do I give PV, PMT and FV?
Think from the point of view of the person in the question. Money that comes to them is positive, money they pay out is negative. A loan: PV positive (they receive it), PMT negative (they repay), FV 0. A savings plan: PV 0 or negative (initial deposit), PMT negative (monthly deposits), FV positive (what they get back).
What is the difference between P/Y and C/Y?
P/Y is how many payments per year; C/Y is how many times interest is compounded per year. For most IB questions they are equal (monthly payments, monthly compounding). A question like "quarterly payments, interest compounded monthly" has P/Y = 4 and C/Y = 12.
Is the TVM solver allowed in IB exams?
Yes. It is a standard function of every approved GDC and the AI syllabus explicitly expects technology for these problems. The AA syllabus does not include financial applications beyond the compound interest formula.
Can I find the interest rate or the number of years?
Yes: fill the other six fields and solve for I% or for N. N will come out as a decimal number of periods: round up to the next whole period for "how long until she has at least ...".

Practise it

Other calculator skills

Written by Pietro Meloni, PhD, IB Mathematics and Physics tutor. Keystrokes checked on TI-Nspire CX II OS 6, Casio fx-CG50 OS 3 and TI-84 Plus CE OS 5; older systems may number the menus differently. Not affiliated with the International Baccalaureate Organization, Texas Instruments or Casio. Found a key that has moved? Write to pietro@pietromeloni.com.

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