E X A M P L E Ann saves $$3,000$ a year from age $25$ to $34$ inclusively and invests in an account

earning $8\%$ annually. Ann stops investing at age $34$ but does not withdraw the accumulation until

age $65.$ Ann's accumulation at age $65$ is $$472,300$ even though she only deposited $$30,000.$ In

contrast, Bob saves $$3,000$ a year from age $35$ to $65$ inclusively and invests in an account similar to

Ann's, earning $8\%$ annually. Even though Bob saved $$93,000$ more than Ann, he will have accumu$-$

lated $$102,300$ less than Ann at age $65.$ The deposits and balances for Ann and Bob at age $65$ are

presented in Exhibit $15\mathrm{.}4.$

EXHIBIT $15\mathrm{.}4$ Time$/$Savings Example $($Accumulation at Age $65)$ How do they get the $$472,300$ for anna? $($please show step by step$)$