You are planning for your retirement in $35$ years. At that time you want to have enough saved to be able to afford to spend $$160,000$ per year $($starting at time $36)$ for $23$ years $($if you live longer than $23$ years your kids will have to support you$).$

How much will you need to have saved by time $35$ if the expected interest rate from time $35$ to $58$ is $11$ percent per year?