Respuesta :
In order to find the time required, we can use the formula below for compound interest:
[tex]I=P(1+r)^t-P[/tex]Where I is the interest, P is the principal, r is the rate and t is the time.
So, for I = 143.5, P = 3500 and r = 0.0825, we have:
[tex]\begin{gathered} 143.5=3500(1+0.0825)^t-3500 \\ 143.5+3500=3500(1.0825)^t \\ 3643.5=3500(1.0825)^t \\ 1.0825^t=\frac{3643.5}{3500} \\ 1.0825^t=1.041 \\ \ln (1.0825)^t=\ln (1.041)_{} \\ t\cdot\ln (1.0825)=\ln (1.041) \\ t=\frac{\ln (1.041)}{\ln (1.0825)} \\ t=\frac{0.0401818}{0.07927318} \\ t=0.5 \end{gathered}[/tex]Therefore it will take 0.5 years to achieve this interest.
