Key Idea: Money that grows or shrinks by the same percentage each period — savings, loans, depreciating cars. On Paper 2 the GDC's TVM solver does the heavy lifting; on Paper 1 you work it by hand.
📈 Compound interest
- future (final) value
- present value — the amount invested
- annual interest rate as a percent
- times compounded per year
- number of years
Compound interest pays interest on the interest, so the balance grows geometrically. Per-period rate = r ÷ k, and the number of periods = k × n. Half-yearly k = 2, quarterly k = 4, monthly k = 12 — and annual is just k = 1, giving FV = PV(1 + r/100)ⁿ.
📉 Depreciation = decay
- starting value
- annual rate lost as a percent
- number of years
✏️ IB-style worked examples
IB-style question — compound interest, compounded quarterly
$6000 is invested at 5% per year, compounded quarterly. Find its value after 4 years, to the nearest dollar.
Step by step:
Quarterly → k = 4. Per-period rate = 5 ÷ 4 %; periods = 4 × 4 = 16.
Simplify inside the bracket.
Work it out on the GDC.
≈ $7319.
IB-style question — depreciation from a model
A van is worth V = 28 000(0.85)ᵗ dollars, t years after purchase. (a) Write down the annual rate of depreciation. (b) Find its value after 5 years, to the nearest dollar.
Step by step:
(a) The multiplier is 0.85, so the rate lost is 1 − 0.85.
(b) Substitute t = 5.
Work it out on the GDC.
(a) 15% per year. (b) ≈ $12 424.
IB-style question — TVM solver, find how long (Paper 2)
$9000 is invested at 3.6% per year, compounded monthly. Find the number of whole years until it first exceeds $11 000.
Step by step:
Enter I% = 3.6, PV = −9000, PMT = 0, FV = 11000, P/Y = C/Y = 12. Solve for N.
Round up to a whole month, then convert to years.
N is in months (P/Y = 12), so divide by 12 — and round up, a part-period doesn't count.
6 years.
IB-style question — TVM solver, find the rate (Paper 2)
$4000 grows to $5000 in 5 years, compounded quarterly. Find the annual interest rate.
Step by step:
List the TVM inputs — that list is your working. 5 years quarterly → N = 5 × 4 = 20.
Leave I% blank, put the cursor on it and solve.
Annual rate ≈ 4.49%.
Important: In the TVM solver, money you pay out (invest) is negative — PV = −4000, not 4000 — or the solver errors. Match P/Y = C/Y to the question (quarterly → 4, monthly → 12), and remember N counts periods: N = years × frequency. When the answer is N, round up for "how long until".
Tap each card to reveal the answer.
Exam Tips
- Compound interest: FV = PV(1 + r/(100k))ᵏⁿ — divide the rate by k, raise to k × n.
- Depreciation multiplies by (1 − rate) each year; rate lost = 1 − multiplier.
- TVM signs: money invested → PV negative; PMT = 0 when there are no regular deposits.
- Set P/Y = C/Y = compounding frequency, and N = years × frequency.
- Paper 1 → work by hand; Paper 2 → leave the unknown blank, solve with ALPHA + ENTER (round N up).