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Financial Maths, STD2 F5 2021 HSC 21

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 deposit of $500.

Julie has created a spreadsheet to show the activity in her savings account. The details for the first 6 months are shown.
 

   

By finding the monthly rate of interest, complete the final row above for the 7th month.  (3 marks)

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`15\ 624.20, 23.44, 16\ 147.64`

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`\text{Monthly interest rate} = \frac{18.75}{12\ 500} = 0.0015 =\ text{0.15%}`

♦ Mean mark 43%.
 

`\text{Row 7 calculations:}`

`\text{Beginning balance}` `= 15\ 624.20`
`\text{Monthly interest}` `= 15\ 624.20 \times 0.0015`
  `= 23.44`

 

`\text{End of month balance}` `= 15\ 624.20 + 23.44 + 500`
  `= 16\ 147.64`

Financial Maths, STD2 F5 2016 HSC 28d

The table gives the contribution per period for an annuity with a future value of $1 at different interest rates and different periods of time. 
 

2ug-2016-hsc-q28_31
 

Margaret needs to save $75 000 over 6 years for a deposit on a new apartment. She makes regular quarterly contributions into an investment account which pays interest at 3% pa.

How much will Margaret need to contribute each quarter to reach her savings goal?  (2 marks)

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`$2865`

Show Worked Solution

`text(Periods) = 6 xx 4 = 24`

♦ Mean mark 40%.

`text(Interest rate) = 1/4 xx 3 = 0.75text(%)`

`=>\ text(Table factor = 0.0382)`

`(text(i.e. 3.82 cents contributed per)`

  `text(quarter = $1 after 6 years))`

 

`:.\ text(Quarterly contribution)`

`= 75\ 000 xx 0.0382`

`= $2865`