Practice Problem $3$: Johnny Saving and Benny Broke both start with $$50,000$ in their retirement accounts and plan to let their money grow until they reach $$1,000,000.$

Johnny Saving invests wisely in a low$-$cost index fund, earning an $8\%$ annual return with minimal fees.

Benny Broke, on the other hand, invests in high$-$fee mutual funds and frequently trades stocks, which reduces his return by $2\%$ annually$-$giving him a $6\%$ return instead.

Questions:

a$)$ How much money will Johnny end up with after $30$ years?

b$)$ How much money will Benny end up with after $30$ years?

c$)$ How many years will it take for Johnny to reach $$1,000,000$ at an $8\%$ annual return?

d$)$ How many years will it take for Benny to reach $$1,000,000$ at a $6\%$ annual return?

e$)$ How many extra years does Benny have to wait due to his higher fees and lower return?

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