The finance solver does the algebra: On Paper 2 the TI-84 TVM Solver (APPS → Finance → 1: TVM Solver) handles any compound-interest problem.
Fill in everything you know, leave the unknown blank, then put the cursor on it and solve.
- N
- the total number of periods = years × compounding frequency (e.g. 3 years, quarterly → N = 12).
- I%
- the annual interest rate, as a percent (5, not 0.05).
- PV
- present value — the amount you start with. Enter it NEGATIVE (money leaving you to invest).
- FV
- future value — the amount at the end. It comes back to you, so it is POSITIVE.
- PMT
- the regular payment each period — enter 0 when there are no extra deposits.
- P/Y, C/Y
- periods per year — annually 1, half-yearly 2, quarterly 4, monthly 12. Set both the same.
Sign convention: Money you pay out (invest) is negative; money you receive is positive.
Get the signs wrong and the solver returns an error or a negative answer.
Solve for I%: To find an unknown interest rate: enter N, PV (negative), PMT = 0, FV (the target), and P/Y = C/Y = the compounding frequency.
Leave I% blank, put the cursor on it, and solve.
IB-style question — find the rate
$5000 is invested, compounded quarterly. After 4 years it has grown to $6500.
Find the annual interest rate, to two decimal places.
Step by step
- Start from the compound-interest formula — it tells you which number goes in which field.
- Read off the values: PV = 5000, FV = 6500, k = 4 (quarterly), n = 4 years, so N = kn = 16. The unknown is the annual rate r.
- On the GDC TVM solver enter N = 16, PV = −5000, PMT = 0, FV = 6500, P/Y = C/Y = 4, leave I% blank and solve. The I% it returns IS the annual rate.
- By hand instead: divide, take the 16th root for the per-quarter rate, then multiply by 4 for the year.
Final answer
r ≈ 6.61% per year.
Match P/Y and C/Y to the question: Annually → P/Y = C/Y = 1; half-yearly → 2; quarterly → 4; monthly → 12. And N counts periods, so N = years × frequency.
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Solve for N: To find how long an investment takes: fill I%, PV (negative), PMT = 0, FV, and P/Y = C/Y, then solve for N.
N comes out in periods — divide by the frequency for years, and round up for "how long until".
IB-style question — find the time
$8000 is invested at 4.5% per year, compounded monthly.
Find the number of whole years until it first exceeds $10 000.
Step by step
- Set up: I% = 4.5, PV = −8000, FV = 10000, P/Y = C/Y = 12. Solve for N.
- Round up to a whole month, then convert to years.
- Check.
Final answer
5 years (60 months).
Periods vs years: If P/Y = 12, N is in months — divide by 12 for years. Always round up (a part-period doesn't count as reached).