Assume compound interest unless otherwise stated. Must be solved with factors and$/$or Excel PV$,$ FV$,$ PMT$,$ NPER, or interest rate functions; you may not use NPV$.$

Formulation $($including factors$)/$ calculations must be shown. For each problem, include a cash flow diagram. If Excel is used for calculations, include the Excel formula$($s$)$ used.

savings and new revenues. At $$18\%$ interest, how many years will it take until the improvement project breaks even?

b$.$ A project has a complex set of cash flows associated with it$,$ with the net cash flow each years as follows: time $0$: $-$$$80$k; time $1$: $$40$k; time $2$: $$200$k; time $3$: $-$$$100$k; time $4-6$: $-$$$110$k each year; time $7$: $$30$k; time $8$: $$500$k$.$ At $i=10\%,$ find the equivalent $P$ for this project.