Key Idea: Compound interest is a geometric sequence: your money grows by the same ratio each compounding period.
Three things IB tests on this topic:
📐 The compound interest formula
What each part of the formula means:
FV
Future Value — the amount at the end of the investment period.
→ Solve for this when finding the final amount
PV
Present Value — the starting amount.
→ Enter as negative on GDC (money going out)
r / 100k
Interest rate per compounding period as a decimal.
→ Annual rate ÷ 100 ÷ k
kn
Total number of compounding periods.
→ Periods per year × number of years
Both give the same answer. On Paper 2, the TVM solver is faster and less error-prone — but you must list all input values (N, I%, PV, PMT, FV, P/Y, C/Y). That list is your working. No list = no method marks.
📊 Compounding frequency
✏️ IB-style worked examples
IB-style: find value, then find when target is reached
Amara invests $9000 in an account that offers 7% per annum compounded <strong>annually</strong>.<br><br>(i) Find the value of the investment after 5 years, to the nearest $100.<br>(ii) Find the number of years required for the investment to reach $20 000.
Step by step:
(i) k = 1 (annual), PV = 9000, r = 7, n = 5
(ii) Set FV = 20 000 and solve for n:
OR: TVM inputs: N = ?, I% = 7, PV = −9000, FV = 20000, PMT = 0, P/Y = 1, C/Y = 1
GDC gives n = 11.90... → must be a whole number, round up: n = 12 years
(i) 12 600 (ii) 12 years
IB-style: find the minimum interest rate (monthly compounding)
Bill invests $9000 at r% per annum compounded <strong>monthly</strong>, where r is to 2 decimal places.<br><br>Find the minimum value of r needed to reach $20 000 after 10 years.
Step by step:
Monthly compounding: k = 12, so total periods = 12 × 10 = 120
GDC TVM: N = 120, PV = −9000, FV = 20000, PMT = 0, P/Y = 12, C/Y = 12
Solve for I% → GDC gives 8.01170...
r must be to 2 dp and must be enough to reach the target → round up: r = 8.02%
Minimum r = 8.02% per annum
Depreciation — find value after n years
A car costs $18 000 and depreciates at 15% per year. Find its value after 4 years.
Step by step:
Rate of loss = 15% → multiplier = (1 − 0.15) = 0.85 each year
18 000 × 0.52201 = 9 396.18
9 396.18 (nearest cent)
Round UP for 'how many years' questions — if GDC gives n = 11.9, the answer is 12 (not 11). The target must actually be reached. Sign convention (GDC): Money going in is negative. Invest 9000 → PV = −9000. FV comes out positive. Monthly for 10 years: N = 120 and C/Y = P/Y = 12 — not N = 10. Forgetting to adjust N loses the method mark. Show TVM inputs: List N, I%, PV, PMT, FV, P/Y, C/Y. This is your written working — no list = no method marks. Nearest $100 rounding: Only round at the very end. Carry full precision in intermediate steps.