Mr Ngomane started saving R2400 per month, two years ago so that he can take this money and invest it with a bank in order to put down a deposit when buying a car. He approached a bank that offered him 12.5% interest per annum, compound interest for a period of 2,5 years on the total amount saved.

$$i_{monthly} = \frac{0.125}{12}$$ $$i_{monthly} = 0.01041666...$$

The monthly interest rate is approximately 0.0104.

6.2.2 Differentiate between interest and interest rate.

Interest is the actual amount of money earned on an investment or paid on a loan. It is typically expressed in currency units (e.g., Rands).
The interest rate is the percentage at which interest is calculated over a specific period. It is expressed as a percentage (e.g., 12.5% per annum).

6.2.3 Determine how much he would be able to invest with the bank if he invests the entire amount.

$$\text{Total amount saved} = \text{Monthly saving} \times \text{Number of months}$$ $$\text{Total amount saved} = \text{R}2400 \times 24$$ $$\text{Total amount saved} = \text{R}57600$$

He would be able to invest R57600.

6.2.4 Determine how much he will earn at the end of the investment period.

$$P = \text{R}57600$$ $$i = \frac{0.125}{12}$$ $$\text{Investment period} = 2.5 \text{ years} \times 12 \text{ months/year} = 30 \text{ months}$$ $$n = 30$$

$$A = 57600 \left(1 + \frac{0.125}{12}\right)^{30}$$ $$A = 57600 (1 + 0.01041666...)^{30}$$ $$A = 57600 (1.01041666...)^{30}$$ $$A = 57600 \times 1.37000607...$$ $$A = 78912.3456...$$

He will earn approximately R78912.35 at the end of the investment period.

6.2.5 Determine how much interest he will earn at the end of the period.

$$\text{Interest earned} = \text{Final amount} - \text{Principal amount}$$ $$\text{Interest earned} = \text{R}78912.35 - \text{R}57600$$ $$\text{Interest earned} = \text{R}21312.35$$

He will earn R21312.35 in interest.