Find the time in which she 12500 will produce 3246.40as compound interest at 8% per annum,interest compounded annually.

Dear Student,

Please find below the solution to the asked query:

Given :  Principle amount =  P  = 12500 , Compound interest =  3246.40 , Rate = r = 8 % per annum compounded annually

Let Time ( In years ) =  t

We know formula for Compound interest when compounded annually :

Compound interest = $\mathrm{P}{\left(1+\frac{\mathrm{r}}{100}\right)}^{\mathrm{t}} -\mathrm{P}$ , So

$$\begin{gathered} 3246.40 = 12500{\left(1+\frac{8}{100}\right)}^t -12500 \\ \Rightarrow 15746.4 = 12500{\left(1+\frac{2}{25}\right)}^t \\ \Rightarrow \frac{15746.4}{12500} = {\left(\frac{27}{25}\right)}^t \\ \Rightarrow \frac{{\displaystyle \frac{15746.4}{0.8}}}{{\displaystyle \frac{12500}{0.8}}} = {\left(\frac{27}{25}\right)}^t \\ \Rightarrow \frac{{\displaystyle 19683}}{{\displaystyle 15625}} = {\left(\frac{27}{25}\right)}^t \\ \Rightarrow {\left(\frac{27}{25}\right)}^3 = {\left(\frac{27}{25}\right)}^t \end{gathered}$$
Compare both side we get :

t  =  3

Therefore,


Time ( In years ) = 3 years                                                     ( Ans )


Hope this information will clear your doubts about topic.

If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.

Regards