Your beloved grandmother gave you a graduation gift of $$1,000$ to entice you to start saving for retirement. Yet, she put a condition: you have to start considering investing for retirement according to the following $2$ alternatives. Depending on your analysis and generated insights she will give you the $$1$k assume that she gives you the $$1,000$ at the start of your $22$ year $($i$.$e$.,22$ years old$).$ You invest the $$1,000$ as soon as you receive it$.$

You want to compare two alternatives to save for retirement:

A$-$ You start investing at the START of the year $23($i$.$e$.,23$ years old$)$ and your last contribution is at the START of the year $34($ie$.,34$ years old$)$

B$-$ You start investing at the start of the year $34($i$.$e$.,34$ years old$)$ and your last contribution is at the start of the year $65($ie$.,65$ years old$)$

In both scenarios you plan to retire at the END of the year $65($i$.$e$.,65$ years old$)$

With the current annual investment, at what interest rate would you be indifferent between A and B$?($Tip$,$ use goal seek, solver, data$-$table or manually$)$ What is the Diff A$-$B of the Total amount contributed?