5.1 Thabile buys a cement mixing machine from a hardware shop on hire purchase at a simple interest rate of 21% per annum - NSC Technical Mathematics - Question 5 - 2022 - Paper 1

To find out how many metal pellets are produced on the first day, we simply take the initial production amount:

• Initial production = 500 pellets
• Increase = 500 pellets * 1.25 = 625 pellets

Thus, the number of metal pellets produced on the first day is 625.

The production increases at a compound rate of 25% per day. We can use the formula for compound growth:

$A = P(1 + r)^n$ Where:

• A = Amount after n days
• P = Initial number of pellets (500)
• r = Rate of increase per day (0.25)
• n = Number of days (10)

Step 1: Substitute values into the formula.

$A = 500(1 + 0.25)^{10}$

Step 2: Calculate.

$A = 500(1.25)^{10} \approx 4665.61$

Rounding gives approximately 4666 pellets produced on the tenth day.

Zane's investment can be calculated using the formula for compound interest:

1. For the first 2 years at 6.78%: $A_1 = P(1 + i/n)^{nt}$ Where:

• n = number of compounding periods (12 months)
• t = the number of years (2)

Thus, $A_1 = P \left(1 + \frac{6.78}{12 \times 100} \right)^{24}$

2. For the next 1.5 years at 5.20%: $A_2 = P(1 + i/n)^{nt} = 50,962.58$

The final value of the investment after 3.5 years can be expressed in terms of the initial amount Z: $50,962.58 = P \left(1 + \frac{6.78}{12 \times 100} \right)^{24} \left(1 + \frac{5.20}{4}\right)^{6}$

By isolating P, we can calculate the initial investment Zane made.