For each scenario, identfity the type of finanical problem, outline the formulas necessary to solve each question, and then compute the solution? $1.$ A bank account that offers $10$ percent of monthly compounded interest, you want to deposit $$500$ at the end of each month, how much money will be in your account in $54$ years?

$2.$ Stacy wishes to provide her daughter with an annuity of $$5000$ for $10$ years. How much should Stacy invest now at the end of

each year, at and APR of $8\%$ per year, compounded annually for the next five years, so that the daughter can withdraw $$5,000$ at the beginning of each year for $10$ years?

$3.$ You want to buy a $$25,000$ Subaru car. You will put $$2000$ down payment,

and a bank offers a loan at an interest of $3\mathrm{.}5\%$ for five years. What will your monthly payment be if you pay at the beginning of each month? What is the total interest amount that you will be paying at the end of $5$ years.

$4.$ You deposit $$500$ at the end of each month into an account earning $3\%$ interest compounded monthly. How much will you have in the account in $35$ years?

$5.$ To accumulate $$500,000$ for retirement in $30$ years at a $7\%$ annual interest compounded monthly, how much needs to be deposited into the account at the end of each month?

$6.$ You're currently $22$ and aiming for financial independence at $50,$ planning to withdraw $$6,000$ monthly for $35$ years, assuming you live until $85.$ To meet this goal, calculate the required monthly investment needed at the end of each month, considering an account offering a $4\mathrm{.}5\%$ APY compounded monthly.