**Question 1**

Emily Dao, 27, just received a promotion at work that increased her annual salary to $37,000. She is eligible to participate in her employer’s 401(k) retirement plan in which the employer matches, dollar for dollar, workers’ contributions up to 5 percent of salary. However, Emily wants to buy a new $25,000 car in three years, and she wants to have enough money to make a $7,000 down payment on the car and finance the balance. Fortunately, she expects a sizable bonus this year that she hopes will cover that down payment in three years.

A wedding is also in her plans. Emily and her boyfriend, Paul, have set a wedding date two years in the future, after he finishes medical school. In addition, Emily and Paul want to buy a home of their own as soon as possible. This might be possible because at age 30, Emily will be eligible to access a $50,000 trust fund left to her as an inheritance by her late grandfather. Her trust fund is invested in 7 percent government bonds.

- Justify Emily’s participation in her employer’s 401(k) plan using the time-value-of-money concepts by explaining how much an investment of $10,000 will grow to be in 40 years if it earns 10 percent.
- Calculate the amount of money that Emily needs to set aside from her bonus this year to cover the down payment on a new car, assuming she can earn 6 percent on her savings. What if she could earn 10 percent on her savings?
- What will be the value of Emily’s trust fund at age 60 if she takes possession of half of the money ($25,000 of the $50,000 trust fund) at age 30 for a house down payment and leaves the other half of the money untouched where it is currently invested?
- What is the relationship between discounting and compounding?
- List at least two actions that Emily and Paul could take to accumulate more for their retirement (think about interest rate or number of year)Please answer question four and Five only

Question 2

Emily Dao, 27, just received a promotion at work that increased her annual salary to $37,000. She is eligible to participate in her employers’ 401(k) plan to which the employer matches dollar-for-dollar workers contributions up to 5% of salary. However, Emily wants to buy a new $25,000 car in three years and she wants to have enough money to make a $7,000 down payment on the car and finance the balance. Fortunately, she expects a sizable bonus this year that she hopes will cover that down payment in three years.

Also in her plans is a wedding. Emily and her boyfriend, Paul, have set a wedding date two years in the future after he finishes medical school. In addition, Emily and Paul want to buy a home of their own as soon as possible. This might be possible because, at age 30, Emily will be eligible to access $50,000 trust fund left to her as an inheritance by her late grandfather. Her trust fund is invested in 7% government bonds.

1) Justify Emily’s participation in her employer’s 401(k) plan using the time value of money concepts by explaining how much an investment of $10,000 will grow to in 40 years if it earns 10%

2) Calculate the amount of money that Emily needs to set aside from her bonus this year to cover the down payment on a new car, assuming she can earn 6% on her savings. What if she could earn 10% on her savings?

3)What will be the value of Emily’s trust fund at age 60, assuming she takes possession of half of the money ($25,000 of the $50,000 trust fund) at age 30 for a house down payment and leaves the other half of the money untouched where it is currently invested?

4) What is the relationship between discounting and compounding?

Savings:

Savings are the amount picked up from the profits and kept aside for future uncertainties and risks. Savings are done for the future so that any uncertain situation can be tacked by the business from the set-aside funds.

Question 3

Answer to question 1

Step 1

Since you have posted a multiple question, therefore, we will be solving the first question only as per the guidelines. However, if you want the other questions to be solved then kindly repost those questions only or mention the questions to be solved.

A 401 (k) plan is a plan that is qualified and provides a feature to the employee to contribute a portion of the employee’s owns wages in an individual investment account. The employee gets various options to choose from. This 401 (k) plan helps or provides an incentive to the employees to save money for retirement. Also, this plan provides an advantage of tax savings too.

Step 2

TO FIND

The future value of an investment

Step 3

Answer to question 2

1) Calculation of future value

PMT = 10,000

Time = 40 years

Rate = 10%

2) Earnings at 10% savings

Amount = 7,000

Time 3 years

Rate 6%

3) Calculation of amount in trust fund

Investment = 25,000

Interest =7%

Time = 60-30 = 30 years

Answer to question 3

1) The needs of emily are

Car

Wedding

House

The down payment of car can be paid throgh the amount of bonus. House can be bought at age of 30when she will get the amount from the trust. Now considering the situation Emily have to arrange her wedding with paul.Since she got an hike in her salary she can use it to plan some savings by investing in employers 41(K) plan.

If Emily invests $ 10000 then her employer will also contribute $1850 ( 5% of her salary)

The total investment amount will be $11850 which will turn out to be $536322.2 in 40 years

2. If she earna 6 % on her savings = 7000/(1.06^3) = $5787.36

If she earna 10 % on her savings = 7000/(1.06^3) = $5259.21

3. Value of Remaining trusy fund will be = 25000*(1.07^30) = $190306.4

Since she will get the trust fund at age of 30 she will be able to invest it only for 30 years till age of 60.

4. Discounting means attaining the present value of a amount from its future value whereas compounding means deriving the future value of a aum (Present Value).

5. Since emily has a salary of $37000 per annum she can go for some reccuring deposit accounts or she can opt for life insurance policies.