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Time Value of Money Personal Finance Application

Your friend Sue has asked you to help her out as she is developing her financial plan. Help her come up with a plan for her finances and how she can set herself up for financial success!

She has an after tax income of $$48,000$ and budgets $$30,000$ for required expenses. This leaves $$18,000$ to spend on debt and savings annually. $($Assume all annuity payments are in the form of ordinary annuities.$)$

Part A: Debt

Sue has a current balance of $$18,000$ on her credit card. She has a minimum monthly payment of $$500$ and an APR of $18\mathrm{.}0\%($divide by $12$ to get the monthly rate$).$ How many months will it take Sue to pay off her credit card debt?

Suppose Sue needs to purchase a car. She believes she can spend $$550$ a month on a car. She has been approved for a $6\mathrm{.}0\%$ loan $($divide by $12$ for monthly rate$)$ for $48$ months. What is the maximum amount she can spend on a car so as not to exceed her $$550$ a month budget?

Part B: Savings

Sue would like to save up for a down payment on a home she hopes to purchase in $5$ years. If she wishes to have $$20,000$ saved up at the end of five years and can earn $4\mathrm{.}5\%$ annually in her savings account. If she would like to make equal annual deposits, what amount will her deposits need to be in order to reach her goal?

Sue received $$24,000$ as an inheritance from her uncle. He stipulated that she save this money for her $2$ children's college education. She would like to have $$50,000$ saved up in $10$ years. What annual interest must she earn in order to reach this goal $($she will make no additional deposits to this account$)?$

Part C: Offering Advice

Calculate the total annual amount of debt and savings payments Sue has planned in the scenarios above.

If she has any of her $$18,000$ remaining after her credit card, auto loan, and savings are made offer advice on how this should be divided $($make more than the minimum payments or make additional deposits to savings$).$ Be sure to offer reasons on why she should choose to follow your advice rather than spend the cash.