$11\mathrm{.}10$ Deducing a cash flow from its net present value under different interest rates. The net present value $($NPV$)$ of a cash flow c $=($c$1,$ c$2,$ c$3)$ with interest rate r is c$1+$ c$2/(1+$ r$)+$ c$3/(1+$ r$)2.$ With interest rate r $=0,$ the NPV is $1.$ With interest rate r $=0\mathrm{.}05,$ the NPV is $0.$ With interest rate r $=0\mathrm{.}10,$ the NPV is $1.$

Find the cash flow c$.$ You are welcome, indeed encouraged, to use a computer to solve any equations you might need to$.$