Homework answers / question archive / Problem 1   James Street's son, Harold, is 10 years old today

Problem 1   James Street's son, Harold, is 10 years old today

Accounting

Share With

---

Problem 1

 

James Street's son, Harold, is 10 years old today. Harold is already making plans to go to college on his 18th birthday, and his father wants to start putting money away now for that purpose. Street estimates that Harold will need $18,000, $19,000, $20,000, and $21,000 to pay for his freshman, sophomore, junior, and senior years, respectively. He plans to make these amounts available to Harold at the beginning of each of these years.

 

Street would like to make eight annual deposits (the first of which would be made on Harold's 11th birthday, 1 year from now, and the last on his 18th birthday, the day he leaves for college) in an account earning 10% annually. He wants the account to eventually be worth enough to just pay for Harold's college expenses. Any balance remaining in the account will continue to earn the 10%. 

How much will Street have to deposit in this planning account each year to provide for Harold's education?

 

Problem 2

 

You have just had your 30th birthday. You have two children, one of which will go to college 10 years from now and require four beginning-of-the-year payments for college expenses of $10,000, $11,000, $12,000, and $13,000. Your second child will go to college 15 years from now and require four beginning-of-the-year payments for college expenses of $15,000, $16,000, $17,000, and $18,000. In addition, you plan to retire in 30 years. You want to be able to withdraw $50,000 per year (at the end of each year) from an account throughout your retirement. You expect to live 20 years beyond retirement. The first withdrawal will occur on your 61st birthday. 

 

What equal, annual, and end-of-the-year amount must you save for each of the next 30 years to meet these goals, if all savings earn a 13% annual rate of return?

 

Problem 3

 

You are currently 30 years old. You intend to retire at age 60, and you want to be able to receive a 20-year, $100,000 beginning-of-the-year annuity, with the first payment to be received on your 60th birthday. You would like to save enough money over the next 15 years to achieve your objective; that is, you want to accumulate the necessary funds by your 45th birthday.

 

1. If you expect your investments to earn 12% per year over the next 15 years and 10% per year thereafter, how much must you accumulate by the time you reach age 45?
    
2. What equal, annual amount must you save at the end of each of the next 15 years to achieve your objective, assuming you currently have $10,000 available to meet your goal? Assume the conditions stated in section A.