SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Compound Interest, SMB-029

The golf club’s social committee has $3400 invested in an account which pays interest at the rate of 4.4% per annum compounding quarterly.

  1. Show that the interest rate per quarter is 1.1%.  (1 mark)

  2. Determine the value of the $3400 investment after three years.

     

    Write your answer in dollars correct to the nearest cent.  (1 mark)

  3. Calculate the interest the $3400 investment will earn over six years.

     

    Write your answer in dollars correct to the nearest cent.  (2 marks)

Show Answers Only
  1. `text(See Worked Solutions)`
  2. `$3876.97`
  3. `$1020.86`
Show Worked Solution

a.   `text{Interest rate}\ = \frac{4.4}{4} = 1.1text{%  (per quarter)}`
 

b.   `text{Compounding periods}\ (n) = 3 xx 4 =12`

`FV` `= PV(1+r)^n`
  `= 3400(1.011)^12`
  `= 3876.973…`
  `= $3876.97`

 

c.   `text{Compounding periods}\ (n) = 6 xx 4 = 24`

`FV` `= 3400(1.011)^24`
  `= 4420.858…`

 
`text(Interest earned over 6 years)`

`= 4420.86-3400`

`= $1020.86\ \ text{(nearest cent)}`