Mbali invested R10 000 for 3 years at an interest rate of r % p.a., compounded monthly - NSC Mathematics - Question 6 - 2017 - Paper 1

To find the interest rate r, we use the formula for compound interest:

$A = P \left(1 + \frac{r}{n}\right)^{nt}$

Where:

• A = final amount (R12 146,72)
• P = principal amount (R10 000)
• r = interest rate (annual)
• n = number of times interest is compounded per year (12 for monthly)
• t = number of years (3)

Substituting the values into the formula:

$12 146,72 = 10 000 \left(1 + \frac{r}{12}\right)^{36}$

Rearranging to solve for r gives:

1. Calculate the left-hand side:

   • Divide both sides by 10,000: $1.214672 = \left(1 + \frac{r}{12}\right)^{36}$

2. Take the 36th root: $1 + \frac{r}{12} = 1.214672^{\frac{1}{36}}$

3. Calculate: $1 + \frac{r}{12} \approx 1.005416$

4. Isolate r: $\frac{r}{12} = 1.005416 - 1 \approx 0.005416$ $r \approx 0.06500$

5. Convert to percentage: $r \approx 6.5\%$