The Suarezes are looking to retire at age $66,$ as described in detail in the RETIREMENT INFORMATION section of the case study. What balance do they need on the first day of retirement to support this goal, taking their Social Security benefit into account? Assume a $7\%$ investment return on their retirement portfolio before they retire and a $5\%$ return after they retire, and that inflation will average $3\%$ for their entire lives. Assume that Social Security benefits will adjust annually by the inflation rate.

Please include your calculator steps and inputs in your answer.

David & Sofia, both age $40.$

Real rate of return before retirement is $4\%(7\%-3\%=4\%).$

Real rate of return after retirement is $2\%(5\%-3\%=2\%).$

David & Sofia combined annual salary $=$ $$182,000.$

David & Sofia $70\%$ of current earned income $=$ $$182,000$ X $70\%=$ $$127,400.$

David & Sofia combined monthly$/$annual social security benefit $=$ $$4,700$ X $12=$ $$56,400.$

Additional retirement income needed after accounting for annual social security benefit $=$ $$127,400-$$$56,400=$ $$71,000$