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Compound Interest, SMB-013

What amount must be invested now at 6% per annum, compounded quarterly, so that in eighteen months it will have grown to `$14\ 000`? Give your answer to the nearest cent.  (2 marks)

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`$12\ 803.59`

Show Worked Solution

`\text{Interest rate}\ (r) = \frac{0.06}{4} = 0.015\ \ \text{(per quarter)}`

`\text{Compounding periods}\ (n) = \frac{18}{3} = 6`
 

`FV` `=PV(1+r)^n`
`14\ 000` `= PV(1 + 0.015)^(6)`
`:.PV` `= (14\ 000)/1.015^(6)`
  `= $12\ 803.59`