Grade 12 Maths - Finance: Compound Interest & Annuities

Instructions: State the formula before substituting. Identify each variable clearly. Round final answers to 2 decimal places.

Key formulas:

$A = P(1 + i)^n \quad \text{(compound growth)}$

$F = x\left[\frac{(1+i)^n - 1}{i}\right] \quad \text{(future value annuity)}$

$P = x\left[\frac{1 - (1+i)^{-n}}{i}\right] \quad \text{(present value annuity)}$

Section A: Compound Interest (6 marks)

1. R 25 000 is invested at 8.5% p.a. compounded monthly for 6 years. Calculate the final value. (3)

2. How long (in years) will it take R 10 000 to grow to R 18 000 at 9% p.a. compounded quarterly? (3)

Section B: Future Value Annuity (6 marks)

Thandi deposits R 1 500 at the end of each month into a savings account earning 7.2% p.a. compounded monthly.

1. How much will she have after 5 years? (3)

2. How much of this is interest? (1)

3. If she needs R 120 000 after 5 years, calculate the required monthly deposit. (2)

Section C: Present Value / Loan (8 marks)

1. Sipho takes out a home loan of R 850 000 at 11.5% p.a. compounded monthly, to be repaid over 20 years. Calculate the monthly instalment. (4)

2. After 5 years of payments, calculate the outstanding balance on Sipho’s loan. (4)

Total: 20 marks