Simple Interest (HSC SSCE Mathematics Standard): Revision Notes

Worked Example 1: Finding simple interest

Question: Calculate the amount of simple interest paid on an investment of $16000 at $8\%$ simple interest per annum for $3$ years.

Solution:

• Write the simple interest formula:

$I = Prn$

• Substitute $P = 16000$, $r = 0.08$ and $n = 3$ into the formula:

$I = 16000 \times 0.08 \times 3$

• Evaluate:

$I = \$3840$

• Therefore, the simple interest is $3840.

Worked Example 2: Calculating the amount owed

Question: Find the amount owed on a loan of $50000 at $7\%$ per annum simple interest at the end of two years and six months.

Solution:

• Write the simple interest formula:

$I = Prn$

• Substitute $P = 50000$, $r = 0.07$ and $n = 2.5$ into the formula:

$I = 50000 \times 0.07 \times 2.5$

• Evaluate:

$I = \$8750$

• Write the amount owed formula:

$A = P + I$

• Substitute $P = 50000$ and $I = 8750$ into the formula:

$A = 50000 + 8750$

• Evaluate:

$A = \$58750$

• Therefore, the amount owed is $58750.

Worked Example 3: Calculating value of an investment

Question: Joel plans to make an investment of $200000 at $7.5\%$ p.a. simple interest for $2$ years. What is the total value of his investment at the end of $2$ years?

Solution:

• Write the simple interest formula:

$I = Prn$

• Substitute $P = 200000$, $r = 0.075$ and $n = 2$ into the formula:

$I = 200000 \times 0.075 \times 2$

• Evaluate:

$I = \$30000$

• Write the amount owed formula:

$A = P + I$

• Substitute $P = 200000$ and $I = 30000$ into the formula:

$A = 200000 + 30000$

• Evaluate:

$A = \$230000$

• Therefore, the total value is $230000.

Worked Example 4: Constructing a simple interest graph

Question: Draw a graph showing the amount of simple interest earned over a period of $10$ years if $1000 is invested at $8\%$ p.a. Use the graph to estimate the interest earned after $7.5$ years.

Solution:

• Write the simple interest formula:

$I = Prn$

• Substitute $P = 1000$, $r = 0.08$ and $n$ into the formula:

$I = 1000 \times 0.08 \times n$

$I = 80n$

• Draw a table of values for $I$ and $n$:
• Let $n = 0, 2, 4, 6, 8, 10$ and find the interest $(I)$ using $I = 80n$:

• Draw a number plane with $n$ as the horizontal axis and $I$ as the vertical axis
• Plot the points $(0, 0)$, $(2, 160)$, $(4, 320)$, $(6, 480)$, $(8, 640)$ and $(10, 800)$
• Draw a straight line between the points (simple interest graphs are always linear)

• Read the graph to estimate $I$ when $n = 7.5$:

$I = 600 \text{ when } n = 7.5$

• Therefore, the interest after $7.5$ years is approximately $600.