IEB · Grade 12 · Mathematics Paper 1 · Finance, growth and decay
In the print dialog, choose Save as PDF. IEB Grade 12 Finance, Growth and Decay Cheat Sheet Every finance formula and the decision rules for which one to use (about 15 marks of Paper 1). Growth and decay Simple: $A = P (1 + in)$ . Compound: $A = P (1 + i)^{n}$ . Straight-line depreciation: $A = P (1 - in)$ . Reducing balance: $A = P (1 - i)^{n}$ . Match $i$ and $n$ to the compounding period: monthly means $\frac{i}{12}$ and months. Nominal and effective rates $1 + i_{eff} = (1 + \frac{i ^{(m)}}{m})^{m}$ Compare offers with effective rates only. Annuities Future value (savings, sinking funds): $F = \frac{x [( 1 + i ) ^{n} - 1 ]}{i}$ Present value (loans, retirement income): $P = \frac{x [ 1 - ( 1 + i ) ^{- n} ]}{i}$ The formulae assume the first payment is one period from now and the last at the end of $n$ periods. The IEB does not examine variations of the two formulae. Outstanding balance = present value of the payments still to come. Extra payment into a loan: subtract it from the outstanding balance at that time, then find the new instalment over the payments left. Sinking fund target = future cost (inflation) $-$ scrap value (depreciation). Finding $n$ Isolate the power, then $n = \frac{lo g ( \dots )}{lo g ( 1 + i )}$ . PV: $(1 + i)^{- n} = 1 - \frac{P i}{x}$ . FV: $(1 + i)^{n} = 1 + \frac{F i}{x}$ . Non-whole $n$ : that many full payments plus a smaller final payment = (balance after the last full payment) $\times (1 + i)$ . Which formula? Lump sum now, one value later: growth formula. Equal payments building up to a lump sum later: FV annuity. Equal payments paying off a lump sum now: PV annuity. Know by heart When to use FV versus PV Outstanding balance as the PV of the remaining payments The final-payment method when $n$ is not a whole number The effective-rate conversion (not on the information sheet) On the formula sheet Simple and compound growth and decay formulae FV and PV annuity formulae Common traps Rounding the rate or payment before the next step. Counting payments wrongly when they start now or stop early. Subtracting an extra payment from the original loan instead of the balance at that time. Asking for $i$ in an annuity: it is never examined.
Global Tutors is not affiliated with or endorsed by the Independent Examinations Board (IEB). Our notes and practice papers are original and are not official IEB material. We check every answer, but mistakes can slip through. If you spot one, please report it and we'll fix it. Always check against your teacher's notes and official IEB papers. Being checked by our tutors

IEB Grade 12 Finance, Growth and Decay Cheat Sheet

Every finance formula and the decision rules for which one to use (about 15 marks of Paper 1).

Growth and decay

Simple: $A = P (1 + in)$ . Compound: $A = P (1 + i)^{n}$ .
Straight-line depreciation: $A = P (1 - in)$ . Reducing balance: $A = P (1 - i)^{n}$ .
Match $i$ and $n$ to the compounding period: monthly means $\frac{i}{12}$ and months.

Nominal and effective rates

$1 + i_{eff} = (1 + \frac{i ^{(m)}}{m})^{m}$
Compare offers with effective rates only.

Annuities

Future value (savings, sinking funds): $F = \frac{x [( 1 + i ) ^{n} - 1 ]}{i}$
Present value (loans, retirement income): $P = \frac{x [ 1 - ( 1 + i ) ^{- n} ]}{i}$
The formulae assume the first payment is one period from now and the last at the end of $n$ periods. The IEB does not examine variations of the two formulae.
Outstanding balance = present value of the payments still to come.
Extra payment into a loan: subtract it from the outstanding balance at that time, then find the new instalment over the payments left.
Sinking fund target = future cost (inflation) $-$ scrap value (depreciation).

Finding $n$

Isolate the power, then $n = \frac{lo g ( \dots )}{lo g ( 1 + i )}$ .
PV: $(1 + i)^{- n} = 1 - \frac{P i}{x}$ . FV: $(1 + i)^{n} = 1 + \frac{F i}{x}$ .
Non-whole $n$ : that many full payments plus a smaller final payment = (balance after the last full payment) $\times (1 + i)$ .

Which formula?

Lump sum now, one value later: growth formula.
Equal payments building up to a lump sum later: FV annuity.
Equal payments paying off a lump sum now: PV annuity.

Know by heart

When to use FV versus PV
Outstanding balance as the PV of the remaining payments
The final-payment method when $n$ is not a whole number
The effective-rate conversion (not on the information sheet)

On the formula sheet

Simple and compound growth and decay formulae
FV and PV annuity formulae

Common traps

Rounding the rate or payment before the next step.
Counting payments wrongly when they start now or stop early.
Subtracting an extra payment from the original loan instead of the balance at that time.
Asking for $i$ in an annuity: it is never examined.

IEB Grade 12 Finance, Growth and Decay Cheat Sheet

Growth and decay

Nominal and effective rates

Annuities

Finding n

Which formula?

Know by heart

On the formula sheet

Common traps

Finding $n$