Question textTotal: 4 marks] Answer the following questions by filling in the blanks. Don't use any spaces, commas or "$" signs. Give answers as fractions using the forward slash (e.g. 1/2 or 3/4) if the answer is not an integer. Do NOT use brackets unless specified. Use - for any negatives. [Total: 2+2 = 4 marks] Lin’s brother bought a boat priced at $54850, on a hire purchase agreement, with the following terms 30% deposit Monthly payments of $950 for 4 years a. Show that the total amount paid for the boat is $62055 by completing the following step. (2 marks) A= A= Answer 1 Question 5[input] + 950 × Answer 2 Question 5[input] = $62055. b. Calculate: (2 marks)i. The total amount of interest paid.I= I= $Answer 3 Question 5[input]ii. The annual flat rate of interest, correct to 2 decimal places.r= r= Answer 4 Question 5[input]%

Question

Question textTotal: 4 marks] Answer the following questions by filling in the blanks. Don't use any spaces, commas or "$" signs. Give answers as fractions using the forward slash (e.g. 1/2 or 3/4) if the answer is not an integer. Do NOT use brackets unless specified. Use - for any negatives. [Total: 2+2 = 4 marks] Lin’s brother bought a boat priced at $54850, on a hire purchase agreement, with the following terms 30% deposit Monthly payments of $950 for 4 years a. Show that the total amount paid for the boat is $62055 by completing the following step. (2 marks) A= A= Answer 1 Question 5[input] + 950 × Answer 2 Question 5[input] = $62055. b. Calculate: (2 marks)i. The total amount of interest paid.I= I= $Answer 3 Question 5[input]ii. The annual flat rate of interest, correct to 2 decimal places.r= r= Answer 4 Question 5[input]%

BlackTom AI · Accepted Answer

Start by identifying the given data: boat price P = 54850, deposit rate = 30%, monthly payment = 950, term = 4 years.
Step 1: Compute the deposit amount. 30% of 54850 is 0.30 × 54850 = 16455. This is the cash deposit.
Step 2: Determine the amount financed (the principal for the installments). Subtract the deposit from the boat price: 54850 − 16455 = 38395.
Step 3: Convert the loan term to months to match the monthly payments. 4 years × 12 months/year = 48 months.
Step 4: Calculate the total of all monthly payments. 950 × 48 = 45600. This is the total paid via installments over the term.
Step 5: Find the total amount paid for the boat on hire purchase. Add the deposit to the total of monthly payments: 16455 + 45600 = 62055. This confirms the first blank’s value when expressed as 16455 + 950 × 48 = 62055.
Step 6: Compute the total interest paid over the term. Subtract the boat price (the cash cost) from the total amount paid: 62055 − 54850 = 7205. This is the total interest I.
Step 7: Determine the annual flat rate of interest. The flat rate formula is r = I / (P × t), where P is the principal financed and t is the time in years. Here, P = 38395 and t = 4 years, so r = 7205 / (38395 × 4).
Step 8: Perform the denominator calculation: 38395 × 4 = 153580. Then r = 7205 / 153580 ≈ 0.04696.
Step 9: Convert the rate to a percentage and round to two decimals as requested: r ≈ 4.70%.
Summary of the intermediate values you can fill in:
- Answer 1 (deposit part of A) = 16455
- Answer 2 (months in term) = 48
- Answer 3 (total interest) = 7205
- Answer 4 (annual flat rate, percent) ≈ 4.70
Note: All steps used standard hire purchase arithmetic: deposit deduction, monthlies over the term, aggregation of payments, then interest and flat rate calculation using the financed principal and term.

MUF0141 Fund. Mathematics Unit 1 - Semester 1, 2025

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