Question

Find the principal needed now to get the given amount; that is, find the present value,To get $120 after 3 1/4 years at 9% compounded continuouslyThe present value of $120 is $(Round to the nearest cent as needed.)

Answer 1

`\$89.57`

1) Considering the given data, let's turn that mixed number into a decimal form. 3 1/4 is the same as 3.25.

2) Now, we can plug all the data we were told.

`\begin{gathered} 120=P_0e^(0.09*3.25) \\ Pe^(0.09* \:3.25)=120 \\ (Pe^(0.09* \:3.25))/(e^(0.2925))=(120)/(e^(0.2925)) \\ P=(120)/(e^(0.2925)) \\ P=89.56742\approx89.57 \end{gathered}`

Note that we had to round it off to the nearest cent as requested.