An Individual Retirement Account $($IRA$)$ is an annuity that is set up to save for retirement. IRAs differ from TDAs in that an IRA allows the participant to contribute money whenever he or she wants, whereas a TDA requires the participant to have a specific amount deducted from each of his or her paychecks.

When Shannon Pegnim was $14,$ she got an after$-$school job at a local pet shop. Her parents told her that if she put some of her earnings into an IRA, they would contribute an equal amount to her IRA. That year and every year thereafter, she deposited $$500$ into her IRA. When she became $25$ years old, her parents stopped contributing, but Shannon increased her annual deposit to $$1,000$ and continued depositing that amount annually until she retired at age $65.$ Her IRA paid $7\mathrm{.}5\%$ interest. Find the following. $($Round your answers to the nearest cent.$)$

$($a$)$ The future value of the account

$

$($b$)$ Shannon's and her parents' total contributions to the account

Shannon $

Shannon's parents $

$($c$)$ The total interest

$

$($d$)$ The future value of the account if Shannon waited until she was $19$ before she started her IRA

$

$($e$)$ The future value of the account if Shannon waited until she was $24$ before she started her IRA

$