Question

Find the time. Round to the nearest month given the following:Principal: $3,500Rate: 8.25%Interest: $143.50

Answer 1

In order to find the time required, we can use the formula below for compound interest:

`I=P(1+r)^t-P`

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:

`\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=(3643.5)/(3500) \\ 1.0825^t=1.041 \\ \ln (1.0825)^t=\ln (1.041)_{} \\ t\cdot\ln (1.0825)=\ln (1.041) \\ t=(\ln (1.041))/(\ln (1.0825)) \\ t=(0.0401818)/(0.07927318) \\ t=0.5 \end{gathered}`

Therefore it will take 0.5 years to achieve this interest.