What is covered in Grade 11 Mathematics Finance, Growth & Decay?

Compound interest, inflation, present and future value. Nominal and effective interest rates.

Is Grade 11 Finance, Growth & Decay tested in Paper 1 or Paper 2?

Grade 11 Mathematics Finance, Growth & Decay is assessed in Paper 1 of the end-of-year examinations, as per the CAPS Mathematics curriculum guidelines.

When is Finance, Growth & Decay taught in Grade 11 Mathematics?

Finance, Growth & Decay is taught in Term 2 of Grade 11 according to the CAPS Annual Teaching Plan (ATP) for Mathematics in South Africa.

Is Grade 11 Mathematics Finance, Growth & Decay on the CAPS curriculum?

Yes. Finance, Growth & Decay is part of the official CAPS Mathematics curriculum for Grade 11, Term 2 in South Africa. The content on MathSciBuddy follows the Annual Teaching Plan (ATP) set by the Department of Basic Education.

Is this Grade 11 Mathematics study material free?

Yes. All chapter notes, definitions, formulas, and worked examples on MathSciBuddy are completely free to read. No account or subscription is needed to access CAPS-aligned study notes.

Grade 11 Mathematics

Grade 11 · Term 2Mathematics

Finance, Growth & Decay

We extend Grade 10 finance to include nominal and effective interest rates, annuities and future value, and present value calculations.

Week 5

6.1 Nominal & Effective Interest Rates, Future Value

Convert between nominal and effective annual rates
Calculate the future value of periodic payments (annuities)
Solve for present value and time period

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Real-World Connection

A bank advertising '12% p.a. compounded monthly' is NOT the same as '12% per year'. The effective rate is higher because of monthly compounding. Understanding this difference prevents expensive surprises when comparing financial products.

Effective Annual Rate from Nominal

i_{\text{eff}} = \left(1+\frac{i_{\text{nom}}}{m}\right)^m - 1

$m$ = number of compounding periods per year; $i_{\text{nom}}$ = nominal annual rate

Future Value of Annuity

F = x\cdot\frac{(1+i)^n - 1}{i}

$x$ = regular payment, $i$ = interest rate per period, $n$ = number of payments

Present Value of Annuity

P = x\cdot\frac{1-(1+i)^{-n}}{i}

The amount needed NOW to fund $n$ future payments of $x$

ℹ️ Note

For monthly payments at annual rate $i$ : use $i_{\text{monthly}}=\frac{i}{12}$ and $n=12\times\text{years}$ . Always match the frequency of the rate to the frequency of payments.

Worked Examples

Worked Example

Effective vs Nominal Rate

Problem

Find the effective annual rate for a nominal rate of 18% p.a. compounded monthly.

Worked Example

Future Value of Annuity

Problem

R500 is invested monthly for 5 years at 9% p.a. compounded monthly. Find the future value.

Activity — 8 Questions

CAPS Cognitive Level Distribution

L1 · Knowledge2 Q

L2 · Routine Procedures2 Q

L3 · Complex Procedures2 Q

L4 · Problem Solving2 Q

L1 · Knowledge1 mark

Find the monthly rate if the annual rate is 12%.

L1 · Knowledge2 marks

State the formula for effective annual rate from nominal rate compounded

m

times.

L2 · Routine Procedures3 marks

Find the effective annual rate for 24% p.a. compounded quarterly.

L2 · Routine Procedures3 marks

R1 000 is saved monthly for 3 years at 6% p.a. compounded monthly. Find the future value.

L3 · Complex Procedures4 marks

How much must be saved monthly for 10 years at 8% p.a. (monthly compounding) to accumulate R200 000?

L3 · Complex Procedures5 marks

A loan of R80 000 is repaid over 5 years at 12% p.a. compounded monthly. Find the monthly payment.

L4 · Problem Solving5 marks

Compare: investing R100 000 at 15% p.a. (simple) for 3 years vs 14% p.a. (compounded monthly) for 3 years. Which is better?

L4 · Problem Solving6 marks

R500 000 is invested now at 10% p.a. compounded monthly. Monthly withdrawals of R6 000 begin immediately. How long before the account is empty?

Functions