Compound Interest, SMB-019

Kelly invests $8 000 at an interest rate of 7.5% per annum, compounding annually.

After how many years will her investment first be more than double its original value, giving your answer to the nearest year? (3 marks)

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`10\ text{years}`

Show Worked Solution

`FV=PV(1+r)^n`

`r=7.5% = 0.075, PV=8000`

`text(Find)\ n\ text(when)\ FV>16\ 000:`

`8000(1+0.075)^n`	`> 16\ 000`
`1.075^n`	`> 2`

`text(Testing possible values:)`

`1.075^10 = 2.06`

`1.075^9 = 1.92`

`:.\ \text{Kelly’s investment will first double after 10 years.}`