You are planning for your retirement in $20$ years. At that time you want to have enough saved to

be able to afford to spend $$140,000$ per year $($starting at time $21)$ for $20$ years $($if you live longer

than $20$ years your kids will have to support you$).$

How much will you need to have saved by time $20$ if the expected interest rate from time $20$ to

$40$ is $11$ percent per year?

$1114870\mathrm{.}91$

Correct response: $1,114,865\mathrm{.}94+-10$

Suppose that at time $20$ you will receive a retirement bonus of $$90,000$ from your company. If

the annual percentage rate $($APR$)$ is expected to be $13$ percent, compounded monthly, from

now until time $20,$ how much would you need to save at the end of each month in order to be

able to make the desired withdrawals at retirement $($i$.$e$.,$ in order to have $$1,114,865\mathrm{.}94,$

including the bonus, saved at time $20)?$