Payouts and Annuities, Part $1$: Frequency of Withdrawals for Annuities.

For this part of the project, you will be looking at the difference that the frequency of withdrawals and compounding makes on payouts from annuities.

A$.\_$ For all parts of this problem, money is invested in a retirement account with an APR of $8\mathrm{.}04\%.($This is close to the average annual return rate of a traditional individual retirement account over the last decade.$)$ You want to be able to withdraw $$24,000$ per year for $20$ years

$2.\_$ How much must you have in the account to start with if compounding and withdrawals are both annual?

$3.\_$ How much must you have in the account to start with if the compounding and withdrawals are both quarterly?

$4.\_$ How much must you have in the account to start with if the compounding and withdrawals are both monthly?

$5.\_$ How much must you have in the account to start with if the compounding and withdrawals are both weekly $($with $52$ weeks per year$)?$

B$.\_$ For all parts of this problem, you have a savings account that earns $3\mathrm{.}9\%$ APR and starts with $$130,000$ in the account. You want to be able to make withdrawals from the account for $15$ years. Round down to the cent for each answer.

$6.\_$ How much can you withdraw each year if compounding is annual?

How much would you then have withdrawn in total over $15$ years?

$7.\_$ How much can you withdraw each quarter if compounding is quarterly?

How much would you then have withdrawn in total over $15$ years?

$8.\_$ How much can you withdraw each month if compounding is monthly?

How much would you then have withdrawn in total over $15$ years?

$9.\_$ How much can you withdraw each week if compounding is weekly?

How much would you have withdrawn in total over $15$ years?