Perpetual Motion is offering a $20\%$ equity stake in their children's dance clothing company. The firm is promising you $$26,000\mathrm{.}00$ every six months forever in

return for your investment. They have asked for $$258,300\mathrm{.}00$ today in exchange for the deal. If this is a fair offer to you, what is the effective annual return

$($EAR$)$ for you in making this deal?

Answer format: Percentage Round to: $0$ decimal places $($Example: $9\%,$ sign required. Will accept decimal format rounded to $2$ decimal places $($ex: $0\mathrm{.}09))$

Ellie wants to endow a college scholarship to honor her late grandmother. She wants to save enough money to support withdrawals of $$15,103\mathrm{.}00$ per year

$($forever$).$ Ellie will save to fund this scholarship for the next $22\mathrm{.}00$ years. The first scholarship withdrawal will be at the time of her last contribution to the

endowment.

While she saves money for the endowment, Ellie can earn $9\mathrm{.}00\%$ APR per year. Once she has funded the endowment, Ellie will move the money into a safe

account that pays $4\mathrm{.}00\%$ per year. What yearly contribution must Ellie make to achieve her goal?

Answer format: Currency: Round to: $2$ decimal places.

A couple saves $$747\mathrm{.}00$ per month $($end of month$)$ for $39\mathrm{.}00$ years. They can earn $8\mathrm{.}00\%$ annual interest with monthly compounding on this account. The

couple wants their retirement account to last for $26\mathrm{.}00$ years.

When they retire, they will move their savings into a money market fund that pays $2\mathrm{.}58\%$ annual interest with monthly compounding.

Assuming they withdraw at the end of the month, what monthly withdrawals will this account support?