Review Problem #$1$:

Jane Jetson recently won the North Carolina lottery and she has $$1,000,000$ currently available. Jane plans to invest the money today in a relatively low risk investment fund that she expects will provide an annual return of $6\%.$ The money in the second account will be used for several purposes.

Jane plans to retire $15$ years from today and she expects that she will live $30$ years after she retires. Jane would like to have $$100,000$ available each year for her first $15$ years of retirement and $$130,000$ each year during her last $15$ years. All retirement withdrawals will be end$-$of$-$year.

In addition to the retirement withdrawals, Jane would like to give $$1,000,000$ to her son Elroy is currently $15$ years old and Jane wants him to receive the money when is $45$ years old.

Jane plans to keep working until she retires. Her top priority financially is to ensure that funds are available for her retirement and for Elroy. If necessary, Jane will contribute additional funds to the account by making annual end$-$of$-$year deposits during her working years. Alternatively, if the $$1,000,000$ is more than is needed to fulfill her plans, Jane would like to make annual end$-$of$-$year withdrawals during her working years. Jane MUST have sufficient funds to fund her retirement and Elroy's legacy.

Determine whether Jane must pay or make withdrawals. Solve for the dollar value of the payment$/$withdrawal$.$