Payouts and Annuities, Part III: Reaching a Goal

For this part of the project, you will be looking at how to plan to save up in order to reach desired payout annuity goal. For each part, consider whether you should round up to the cent or down to the cent.

E$.$ When Riley retires, they would like to be able to withdraw $$1250$ semimonthly $($twice per month$)$ from their retirement account, and do so for $15$ years. Their retirement annuity has a $6\%$ APR.

$19.\_$ How much must Riley have in the account at the time they retire?

$20.\_$ If they start saving $10$ years before retirement, how much will Riley need to deposit

Semimonthly to reach their goal?

How much will they deposit in total over the $10$ years?

$21.\_$ If they start saving $25$ years before retirement, how much will Riley need to deposit

Semimonthly to reach their goal?

How much will they deposit to total over the $25$ years.

$22.\_$ If they start saving $40$ years before retirement, how much will Riley need to deposit

Semimonthly to reach their goal?

How much will they deposit in total over the $40$ years?

F$.$ Pat is going to start a college fund for a child. They want the child to eventually be able to withdraw $$5000$ per quarter for four years. Pat$$s credit union offers a college savings annuity account with a $5\mathrm{.}1\%$ APR.

$24.\_$ How much must Pat have in the account when the child starts college?

$25.\_$ If they start saving $18$ years before the child starts college, how much will Pat need to

Deposit monthly to reach their goal?

How much will they deposit in total over the $18$ years?

$26.\_$ If they start saving $12$ years before the child starts college, how much will Pat need to

Deposit monthly to reach their goal?

How much will they deposit in total over $12$ years?

$27.\_$ If they start savings four years before the child starts college, how much will Pat need to

Deposit monthly to reach their goal?

How much will they deposit in total over the four years?