On January $1,1822,$ Washington I. Winkle received an inheritance of $$500.$ He deposited

this sum into a bank account, and then went to the nearby Chowdownings Tavern for a

drink. The drink was dodgy and Winkle fell asleep for $200$ years.

When Winkle awoke in $2022,$ how much money did he have in the account?

When Winkle awoke in $2022,$ he was still a young man. Suppose his life expectancy is

about $60$ more years. Suppose Winkle wishes to leave a bequest to his future family of

$$500$ million on January $1,2082.$ How much can Winkle spend per year between $2022$ and

the bequest date, and still have enough money to leave the desired bequest?

Assume the expenditures occur on January $1$st of each year. The first expenditure is on

January $1,2022,$ and the last is on January $1,2081.$ Assume that the interest rate is $7\%$ per

year.

Please show formulas