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.

 

  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 be in 40 years if it earns 10 percent.
  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 percent on her savings. What if she could earn 10 percent on her savings?
  3. 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?
  4. What is the relationship between discounting and compounding?
  5. 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)
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