Assume Jacob is $30$ years old and has $35$ more years to work. Currently he doesn$$t have any savings. His

annual income in real terms is $$65,000.$

Assuming a life expectancy of $85$ years, real interest rate throughout of $6\%$ and desired retirement

income of $70\%$ of pre$-$retirement income, prepare a lifetime consumption$-$savings schedule for Jacob.

Specifically calculate the following and then show excel schedule showing lifetime plan.

a$)$ Annual savings and annual consumptions during the $35$ working years, and Accumulated wealth

at the end of the working years $($beginning of retirement years$).$

b$)$ If Jacob plans to take a vacation at the end of his age $80$ and it costs additional $$20,000,$ and he

wants to leave $$30,000$ for charity at the end of his life. How would these affect annual savings

and consumptions? Re$-$prepare the schedule.

c$)$ How would the financial plan change if Jacob already has savings of $$15,000$ today?