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Julie invests $12 500 in a savings account - HSC - SSCE Mathematics Standard - Question 21 - 2021 - Paper 1

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Julie invests $12 500 in a savings account. Interest is paid at a fixed monthly rate. At the end of each month, after the monthly interest is added, Julie makes a de... show full transcript

Worked Solution & Example Answer:Julie invests $12 500 in a savings account - HSC - SSCE Mathematics Standard - Question 21 - 2021 - Paper 1

Step 1

Monthly rate of interest

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Answer

To find the monthly rate of interest, we can use the formula:

Monthly Rate of Interest=Monthly InterestAmount in Account at Beginning of Month×100\text{Monthly Rate of Interest} = \frac{\text{Monthly Interest}}{\text{Amount in Account at Beginning of Month}} \times 100

For the 1st month:

Monthly Rate of Interest=18.7512500×100=0.15%\text{Monthly Rate of Interest} = \frac{18.75}{12 500} \times 100 = 0.15\%

This shows a monthly interest rate of 0.15%. Therefore, we can apply this rate to the 7th month:

The monthly interest for the 7th month can be computed as:

Interest=15624.20×0.0015=23.44\text{Interest} = 15 624.20 \times 0.0015 = 23.44

Hence, the monthly interest that will be added for the 7th month is $23.44.

Step 2

Amount in account at end of month (7th month)

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Answer

To find the amount in the account at the end of the 7th month, we add the deposit and the interest to the amount at the beginning of the month:

Amount in Account at End of 7th Month=15624.20+500+23.44=16147.64\text{Amount in Account at End of 7th Month} = 15 624.20 + 500 + 23.44 = 16 147.64

Thus, the final amount in the account at the end of the 7th month is $16 147.64.

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