# $1570 is invested at 12% p.a. compound interest. After how many years will the investment be worth $23 000?

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The formulae for compound interest is as follows.

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

FV = Future value

PV = Present value

i = interst rate per annum

n = number of years

For our question;

`FV = 23000`

`PV = 1570`

`i = 12% = 0.12`

`n = ??`

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

Take log on both sides.

`log(FV) = log(PV(1+i)^n)`

`logFV = log(PV)+nlog(1+i)`

`log23000 = log1570+nlog(1+0.12)`

`log(23000/1570) = nlog1.12`

`n = 23.687`

*So it will take 24 years for the invesment to reach $23000.*

*Note:*

*I have used the following logarithm rules.*

*log(A/B) = logA-logB*

*log(A^n) = nlogA*

**Sources:**