Question

Question was provided via image upload.

Explanation:

Identify the given values and missing information

The problem states that a finance company charges an interest rate of \(r = 32.95\%\text{ p.a.}\) (per annum) on loans for drones. We are asked to find the simple interest charged for:

• i. 1-year loan (\(t = 1\))
• ii. 2-year loan (\(t = 2\))
• iii. 3-year loan (\(t = 3\))

However, the principal loan amount (\(P\)) is not provided in the visible text of the image. Looking closely at the faint pencil markings on the page, we can see handwritten values:

• For i: "1449.41"
• For ii: "2898.82"
• For iii: "4348.23"

Let us verify if these values correspond to a specific principal \(P\).
Using the Simple Interest Formula:

$$I = P \cdot r \cdot t$$

For \(t = 1\):

$$I = P \cdot 0.3295 \cdot 1 = 1449.41 \implies P = \frac{1449.41}{0.3295} \approx 4398.816$$

For \(t = 2\):

$$I = P \cdot 0.3295 \cdot 2 = 2898.82 \implies P = \frac{2898.82}{0.659} \approx 4398.816$$

For \(t = 3\):

$$I = P \cdot 0.3295 \cdot 3 = 4348.23 \implies P = \frac{4348.23}{0.9885} \approx 4398.816$$

This indicates the calculations are based on a principal loan amount of \(P = \$4398.82\) (or approximately \(\$4400\) depending on rounding). We will express the simple interest both in terms of the principal \(P\) and using the handwritten values shown in the image.

Calculate interest for a 1-year loan

Using the Simple Interest Formula:

$$I = P \cdot 0.3295 \cdot 1 = 0.3295P$$

If the principal is \(P = \$4398.82\):

$$I \approx \$1449.41$$

Calculate interest for a 2-year loan

Using the Simple Interest Formula:

$$I = P \cdot 0.3295 \cdot 2 = 0.659P$$

If the principal is \(P = \$4398.82\):

$$I \approx \$2898.82$$

Calculate interest for a 3-year loan

Using the Simple Interest Formula:

$$I = P \cdot 0.3295 \cdot 3 = 0.9885P$$

If the principal is \(P = \$4398.82\):

$$I \approx \$4348.23$$

Answer:

Question i

The simple interest charged on a 1-year loan is \(0.3295P\) (which is \(\$1449.41\) if the principal loan amount is \(\$4398.82\)).

Question ii

The simple interest charged on a 2-year loan is \(0.659P\) (which is \(\$2898.82\) if the principal loan amount is \(\$4398.82\)).

Question iii

The simple interest charged on a 3-year loan is \(0.9885P\) (which is \(\$4348.23\) if the principal loan amount is \(\$4398.82\)).