Two designs have been proposed for a short$-$span bridge in a rural area, as shown in the following table. The first proposal is to construct th bridge in two phases $($Phase I now and Phase II in $25$ years$).$ The second alternative is to construct it in one phase.

Assuming that the annual interest rate is $4$ percent, use present worth analysis to calculate the present worth $($in dollars$)$ for each alternativ $($Assume all maintenance costs are due at the end of each year.$)$

Alternative $\backslash (\backslash$mathrm$\{$A$\}\backslash$quad $\backslash$mathrm$\{$PW$\}=\backslash$$ $\backslash )$

Alternative $\backslash (\backslash$mathrm$\{$B$\}\backslash$quad $\backslash$mathrm$\{$PW$\}=\backslash$$ $\backslash )$

Determine which alternative is preferred.

Alternative A

Alternative B