# Time Value Problems

 A parent is now planning a savings program to put a daughter through college.  She is 13 and plans to enroll in college in 5 years, and she should graduate 4 years later.  Currently, the annual cost for college is \$15,000 and is expected to increase 4% each year.  The college requires that the costs be paid at the start (hint:  beginning) of each year.  The child now has \$7,500 saved for college in an account and is expected to have a return of 6% annually.  The parent will make five equal payments starting today and where the fifth and final payment will be one year before she starts college and will make no more additional payments.   How much must each of the payments be to fully fund the college cost? Answer the following questions: 1.       What is the expected cost of college in each of the 4 years? 2.       How much will need to be in the account before the first payment to fully pay for college? 3.       How much will the initial savings grow to before the first payment is due? 4.       How much of a gap that will need to be funded? 5.       What will the required payment need to be to fully fund the expected cost and the savings shortfall? 6.       Can you ‘proof’ your work? Problem #1B A parent is now planning a savings program to put a daughter through college.  She is 13 and plans to enroll in college in 5 years, and she should graduate 4 years later.  Currently, the annual cost for college is \$15,000 and is expected to increase 4% each year.  The college requires that the costs be paid at the start (hint:  beginning) of each year.  The child now has \$7,500 saved for college in an account and is expected to have a return of 6% annually.  The parent will make six equal payments starting today and the sixth on the day she starts college and make no more additional payments.   How much must each of the payments be to fully fund the college cost? Tip:  Use PMT function at ‘END’ to solve and not ‘BEGINNING’.  Think about what the ‘END’ parameter is doing to grow the cash flows.  Treat ‘today’ as if the decision to make the investment in the college was 12 months ago and that ‘today’ is the first payment. Answer the following questions: 1.       What is the expected cost of college in each of the 4 years? 2.       How much will need to be in the account before the first payment to fully pay for college? 3.       How much will the initial savings grow to before the first payment is due? 4.       How much of a gap that will need to be funded? 5.       What will the required payment need to be to fully fund the expected cost and the savings shortfall? 6.       Can you ‘proof’ your work?

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