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José takes out a loan of $9000 - HSC - SSCE Mathematics Standard - Question 13 - 2024 - Paper 1

Question 13

José takes out a loan of $9000. Simple interest is charged on the loan. The loan and the interest charged will be repaid by making monthly repayments of $300 over 4... show full transcript

Worked Solution & Example Answer:José takes out a loan of $9000 - HSC - SSCE Mathematics Standard - Question 13 - 2024 - Paper 1

Step 1

Calculate the Total Repayment

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Answer

The total repayment can be computed as follows:

Since José makes monthly repayments of $300 for 4 years, the total number of payments is: $4 \text{ years} \times 12 \text{ months/year} = 48 \text{ months}$ .

Thus, the total repayment is: $300 \text{ dollars/month} \times 48 \text{ months} = 14400 \text{ dollars}$ .

Step 2

Calculate the Total Interest Paid

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Answer

The total interest paid is the total repayment minus the original loan amount:

$\text{Total Interest} = 14400 \text{ dollars} - 9000 \text{ dollars} = 5400 \text{ dollars}$ .

Step 3

Calculate the Simple Interest Rate

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Answer

The simple interest formula is given by: $I = P \times r \times t$ , where:

$I$ is the interest paid,
$P$ is the principal amount (the loan),
$r$ is the interest rate,
$t$ is the time (in years).

Rearranging the formula to find the interest rate $r$ gives us: $r = \frac{I}{P \times t}$ .

Plugging in the values: $r = \frac{5400}{9000 \times 4} = \frac{5400}{36000} = 0.15$ .

Thus, to convert this into a percentage: $r \times 100 = 15\%$ .

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