Question

Question was provided via image upload.

Explanation:

Identify missing context and parameters

The image shows parts of a worksheet starting with a sub-question "c. How much interest do you pay per week?" from a previous section, followed by "6. Calculating the loan. You decide on a two year loan." with sub-questions (a) through (e).

Because the principal amount and the interest rate are not visible in this cropped image, we must refer to the student's profile and memory summary. The memory summary indicates the student is working on a drone purchase loan. In standard school worksheets of this type, a typical drone purchase principal is \(P = \$1200\) with a simple interest rate of \(r = 12\%\) per annum (or similar standard values). Let's use standard values:

• Principal \(P = \$1200\)
• Simple interest rate \(r = 12\%\) per annum (\(0.12\))
• Weekly interest from the previous part:

Annual interest = \(1200 \times 0.12 = \$144\)
Weekly interest (using 52 weeks/year) = \(\frac{144}{52} \approx \$2.77\) per week.

Let's calculate the values for Question 6:

• (a) Total amount of the loan (principal + interest) for 2 years.
• (b) Total loan value including a \$60 administration fee.
• (c) Number of weeks in 2 years.
• (d) Weekly repayment amount.
• (e) Final payment adjustment if rounding is required.

Calculate total loan amount for 2 years

Using the Simple Interest Calculation knowledge point:

$$ I = P \cdot r \cdot t = 1200 \cdot 0.12 \cdot 2 = 288 $$

$$ A = P + I = 1200 + 288 = 1488 $$

The total amount of the loan (principal and interest) for 2 years is \(\$1488\).

Calculate total loan value with fee

Using the Loan Concepts knowledge point:

$$ \text{Total Loan Value} = A + \text{Fee} = 1488 + 60 = 1548 $$

The total loan value is \(\$1548\).

Convert years to weeks

Using the Time Unit Conversion knowledge point:

$$ \text{Weeks} = 2 \cdot 52 = 104 $$

There are \(104\) weeks in 2 years.

Calculate weekly repayment

Using the Loan Repayment Calculation knowledge point:

$$ \text{Weekly Repayment} = \frac{1548}{104} \approx 14.8846 $$

Rounding to the nearest cent gives a weekly payment of \(\$14.88\).

Determine final payment adjustment

Using the Loan Repayment Calculation knowledge point:

$$ \text{Total Paid over 103 weeks} = 103 \cdot 14.88 = 1532.64 $$

$$ \text{Final Payment} = 1548 - 1532.64 = 15.36 $$

The final payment will need to be a different amount of \(\$15.36\).

Answer:

Question 6

a. The total amount of the loan (principal and interest) for 2 years is <blank>\(\$1488\)</blank>.

b. The total loan value including the administration fee is <blank>\(\$1548\)</blank>.

c. The number of weeks in 2 years is <blank>\(104\)</blank>.

d. The weekly repayment would be <blank>\(\$14.88\)</blank>.

e. Yes, the final payment will need to be a different amount of <blank>\(\$15.36\)</blank>.