Revision (Grade 11 NSC Matric Mathematics): Revision Notes

Worked Example: Investment Comparison

Question: Sam wants to invest R3450 for 5 years. Wise Bank offers simple interest at 12,5% per annum. Grand Bank offers compound interest at 10,4% per annum. Which bank gives the better return?

Solution:

Step 1: Calculate using simple interest (Wise Bank)

Write down the known variables:

• $P = 3450$
• $i = 0,125$ (12,5% as a decimal)
• $n = 5$
• $A = P(1 + in)$

Substitute the values:

• $A = 3450(1 + 0,125 \times 5)$
• $A = 3450(1 + 0,625)$
• $A = 3450 \times 1,625$
• $A = \text{R}5606,25$

Step 2: Calculate using compound interest (Grand Bank)

Write down the known variables:

• $P = 3450$
• $i = 0,104$ (10,4% as a decimal)
• $n = 5$
• $A = P(1 + i)^n$

Substitute the values:

• $A = 3450(1 + 0,104)^5$
• $A = 3450(1,104)^5$
• $A = 3450 \times 1,639$
• $A = \text{R}5658,02$

Step 3: Compare and conclude

Grand Bank's compound interest account gives R5658,02, while Wise Bank's simple interest account gives R5606,25.

Answer: Grand Bank offers the better investment option with a higher accumulated balance.

Worked Example: Calculating Required Interest Rate

Question: Bongani invests R30000 and wants to double his money to R60000 in 6 years using compound interest. What interest rate does he need?

Solution:

Step 1: Write down known variables

• $A = 60000$ (target amount)
• $P = 30000$ (initial investment)
• $n = 6$ (years)
• $A = P(1 + i)^n$

Step 2: Substitute and solve for $i$

$60000 = 30000(1 + i)^6$

Divide both sides by 30000:

• $\frac{60000}{30000} = (1 + i)^6$
• $2 = (1 + i)^6$

Take the 6th root of both sides:

• $\sqrt[6]{2} = 1 + i$
• $1,122 = 1 + i$
• $i = 1,122 - 1$
• $i = 0,122$

Step 3: Convert to percentage and round

$i = 0,122 = 12,2\%$

To ensure Bongani doubles his investment, we round up to 12,3% per annum.