Jinhee$$ Ju$,27,$ just received a promotion at work that increased her annual salary to $$$$35,000.$ She is eligible to participate in her$$ employer's $401($k$)$ plan, to which the employer matches$$ dollar$-$for$-$dollar workers' contributions up to five percent of salary.$$ However, Jinhee wants to buy a new $$$$29,000$ car in $4$years$,$ and she wants to save enough money to make a $ $10,000$ down payment on the car and finance the balance.

Also in her plans is a wedding. Jinhee and her$$ boyfriend, Paul, have set a wedding date $22$ years in the$$ future, after he finishes medical school. Paul will have $$$$95,000$ of student loans to repay after graduation. But both Jinhee and Paul want to buy a home of their own as soon as possible. This might be possible because at age$30,$ Jinhee will be eligible to access a $$$$47,000$ trust fund left to her as an inheritance by her late grandfather. Her trust fund is invested in $6$ percent government bonds. a$.$ Justify$$ Jinhee's participation in her$$ employer's $401($k$)$ plan using the time value of money concepts.

Assuming that Jinhee and her employer both contribute five percent of her salary to her$401($k$),$ the amount contributed each year will be $$$enter your response here. $($Round to the nearest$$ dollar.$)$

If$$ Jinhee's salary remains fixed for $40$ years and she earns$8\%$ annually on her$401($k$)$ account, then the value of the account in $40$ years would be $$$enter your response here. $($Round to the nearest$$ cent.$)$

It is in$$ Jinhee's best interest to start contributing t her$401($k$)$ immediately$$ because:$($Select the best choice$$ below.$)$

A$.$

the employer match is$$ "free money" that$$ shouldn't be passed up$.$

B$.$

the employer match is only offered until she turns $30.$

C$.$

she will not be able to buy a house if she does not participate in the$401($k$)$ plan.

D$.$

the employer match is only offered for the first year.

b$.$ Calculate the amount Jinhee needs to save each year for the down payment on a new$$ car, assuming she can earn$8$ percent$8$ percent on her savings.

The amount Jinhee needs to save each year for the down payment on the$$ car, assuming she can earn $8$ percent on her$$ savings, is $$$enter your response here. $($Round to the nearest$$ cent.$)$

Calculate how much she will need to save on a monthly basis assuming monthly compounding.

The amount Jinhee needs to save each month for the down payment on the$$ car, assuming she can earn $8$ percent on her$$ savings, is $$$enter your response here. $($Round to the nearest$$ cent.$)$

For each$$ scenario, how much of her down payment will come from interest$$ earned?

If Jinhee saves for the down payment by putting money away each$$ year, the amount of interest earned by the time she needs the money for the down payment is $$$enter your response here. $($Round to the nearest$$ cent.$)$

If Jinhee saves for the down payment by putting money away each$$ month, the amount of interest earned by the time she needs the money for the down payment is $$$enter your response here. $($Round to the nearest$$ cent.$)$

If Jinhee saves for the down payment by puttting money away each month rather than each$$ year, she will earn $$$enter your response here more in interest over the accumulation period.$($Round to the nearest$$ cent.$)$

c$.$ What will be the value of$$ Jinhee's trust fund at age $60,$ assuming she takes possession of half the money at age $30$ for a house down$$ payment, and leaves the other half of the money untouched where it is currently$$ invested?

If Jinhee leaves half the money in her trust fund when she receives it at age$30,$ the value of the trust fund when she is age $60,$ assuming that she continues to earn the current rate of$$ return, will be $$$enter your response here. $($Round to the nearest$$ cent.$)$