R12 000 is in 'n fonds belê wat rente teen m% p.j., kwartaalliks saamgestel, betaal het - NSC Mathematics - Question 6 - 2022 - Paper 1

To find the value of m, we use the formula for compound interest:

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

Where:

• A is the amount after time t (R13 459)
• P is the principal amount (R12 000)
• r is the annual interest rate (in decimal form, which is m/100)
• n is the number of times interest is compounded per year (4 for quarterly)
• t is the number of years (2 years for 24 months)

Substituting the known values into the formula:

$13 \, 459 = 12 \, 000 \left(1 + \frac{m/100}{4}\right)^{4\cdot2}$

We simplify:

1. Calculate the ratio:

   • $\left(1 + \frac{m}{400}\right)^8 = \frac{13 \, 459}{12 \, 000}$
   • $\left(1 + \frac{m}{400}\right)^8 = 1.121575$

2. Take the eighth root of both sides:

   • $1 + \frac{m}{400} = (1.121575)^{1/8}$
   • $1 + \frac{m}{400} \approx 1.0144$

3. Solve for m:

   • $\frac{m}{400} \approx 0.0144$
   • $m \approx 400 \times 0.0144 = 5.78 \%$

Thus, the interest rate m is approximately 5.78%.