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 $$1,000$ into her IRA. When she became $25$ years old, her parents stopped contributing, but Shannon increased her annual deposit to $$2,000$ and continued depositing that amount annually until she retired at age $65.$ Her IRA paid $7\mathrm{.}5\%$ interest.

If Shannon Pegnim had started her IRA at age $35$ rather than age $14,$ how big of an annual contribution would she have had to have made to have the same amount saved at age $65?($Round your answer to the nearest cent.$)$