Assume you are now $21$ years old and will start working as soon as you graduate from college. You plan to start saving for your retirement on your $25$ th birthday and retire on your $65$ th birthday. After retirement, you expect to live at least until you are $85.$ You wish to be able to withdraw $$59,000($in today's dollars$)$ every year from the time of your retirement until you are $85$ years old $($i$.$e$.,$ for $20$ years$).$ The average inflation rate is likely to be $5$ percent.

Problem $6\mathrm{.}42($a$)$

Your answer is correct.

Calculate the lump sum you need to have accumulated at age $65$ to be able to draw the desired income. Assume that the annual return on your investments is likely to be $10$ percent. $($Round answer to $2$ decimal places, e$.$g$.15\mathrm{.}25.$ Round intermediate value to $3$ decimal places, e$.$g$.359400\mathrm{.}312.$ Do not round factor values.$)$

Lump sum amount accumulated at age $65,$$

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Problem $6\mathrm{.}42($b$)$

Your answer is correct.

What is the dollar amount you need to invest every year, starting at age $25$ and ending at age $65($i$.$e$.,$ for $40$ years$),$ to reach the target lump sum at age $65?($Round factor values to $4$ decimal places, e$.$g$.1\mathrm{.}5212$ and final answer to $2$ decimal places, e$.$g$.1,525\mathrm{.}12.)$

Investment needed to reach the target $

Attempts: unlimited

Problem $6\mathrm{.}42($c$)$

Your answer is incorrect.

Now answer parts a$.$ and b$.$ assuming the rate of return to be $($i$)8$ percent per year, and $($ii$)15$ percent per year. $($Round answers to $0$ decimal places, e$.$g$.1,525.)$

$\backslash$table$[[,8$ percent,$15$ percent$],[$Lump sum needed at age $65,$$$,$$