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 retirement plan to which the employer matches dollar-for-dollar workers' contribution 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 sizeable bonus this year that she hopes will cover the down payment in three years.

A wedding also is also in her plans. Emily and her boyfriend, Paul have set a wedding date two years in the future, after he finished 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 fund is invested in 7% government bonds.

Question 1 

Justify Emily's participation in her employer's 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%.

Question 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?

Question 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?

Question 4 

What is the relationship between discounting and compounding?

Question 5 

List at least two actions that Emily and Paul could take to accumulated more for their retirement

 

Answer:

1. To obtain the value of $10000at the rate of return of10% for a period of 40 years compute the future value(FV) of the cash flowby using the method below;

                FV=PV(1 + r)ⁿ

                Here,

                PV- Present value

                r- rate of return

                n- time duration.

In the case given;

                PV=$10,000; R=10%;N=40years

So,

                FV=10,00091+0.10)ⁿ

FV= 10,000(1.10)⁴⁰

=10,000(45.25926)

FV=452,592.60

Accordingly the future value of $10,000 invested at  time 0 after 40 years at the rate of return of 10%would be $452592.60.

2. To find out the amount to be invested today for down payment of $7000 after 3 years, we need to calculate present value of $7000at the required rate of return. It can be obtained as follows;

                PV=FV/(1 = r)

Here, 

                FV= future value 

                R=required rate of return or discounting rate.

                N= time duration.

So, FV= $7000,r=6%,n=3years.

PV =$7000/(1+0.06)³

PV=$7000/1.191= $5877.34

At the discount rate of 6% Emily requires to set aside $5877.34 for making down payment of $7000after 3 years.

If the rate on the savings is 10% then we need to discount the FV  at the rate of 10%.

 This would be;

PV =$7000/1.331= $5259.20. So if the savings earn rate of return of 10%, then Emily requires to set aside $5259.20 only for making down payment for the car after 3 years.

3. the future value of half the trust fund after 30 years by using the formula;

                FV = PV(1+r)

                Here, PV=25000,R=7000AND N=30YEARS

SO, 

                FV= 25000(1+0.07)³⁰

                FV=25000(1.07)³⁰=25000(7.6123)

                                =$190,306.40

4. Discounting and compounding have inverse relationship. Discounting is  used to calculate the present value of a cash flow whik=le compounding is used to calculate future value of the cash flow.

5.the retirement corpus will be more if it earns higher rate of return and if it is invested for longer duration as invested money would be able to generate higher  returns because of compounding for longer duration at higher rate of return.