Peter and Blair recently reviewed their future retirement income and expense projections. They hope to retire in $29$ years and anticipate they will need funding for an additional $20$ years. They determined that they would have a retirement income of $$62,000\mathrm{.}00$ in today's dollars but that they would actually need $$86,142\mathrm{.}00$ in retirement income $($in today's dollars$)$ to meet all of their objectives.

a$.$ What is their annual shortfall at retirement assuming inflation of $3$ percent per year? Click on the table icon to view the FVIF table:

b$.$ At the time that they retire, how much additional amount must they have accumulated to fund their retirement needs, assuming $3$ percent inflation and a rate of return of $9$ percent? Click on the table icon to view the PVIFA table:

c$.$ Calculate the additional amount that Peter and Blair must save each year for the next $29$ years if they wish to completely fund their income shortfall. Click on the table icon to view the FVIFA table: