Chapter 5, Problem 40P

Fundamentals of Financial Manageme...

15th Edition
Eugene F. Brigham + 1 other
ISBN: 9781337395250

Chapter
Section

Fundamentals of Financial Manageme...

15th Edition
Eugene F. Brigham + 1 other
ISBN: 9781337395250
Textbook Problem

REQUIRED ANNUITY PAYMENTS A father is now planning a savings program to put his daughter through college. She is 13, plans to enroll at the university in 5 years, and should graduate 4 years later. Currently, the annual cost (for everything—food, clothing, tuition, books, transportation, and so forth) is $12,000, but these costs are expected to increase by 6% annually. The college requires total payment at the start of the year. She now has$10,000 in a college savings account that pays 9% annually. Her father will make six equal annual deposits into her account; the first deposit today and the sixth on the day she starts college. How large must each of the six payments be? (Hint Calculate the cost (inflated at 6%) for each year of college and find the total present value of those costs, discounted at 9%, as of the day she enters college. Then find the compounded value of her initial $10,000 on that same day. The difference between the PV of costs and the amount that would be in the savings account must be made up by the father’s deposits, so find the six equal payments that will compound to the required amount.) Summary Introduction To calculate: Equal annual saving that will compound to the required amount. Introduction: Annuity: It is an agreement under which a person pays the lump sum payment or the number of small transactions and in return he receives the amount at later date or upon annuitization. The purpose of the annuity is to not the break the flow of income after retirement. Explanation Compute total cost of college in first year of college. Given, Current cost is$12,000.

Interest rate is 6%.

Number of years is 5.

Formula to calculate cost of first year is,

Costāofāfirstāyear=CurrentācostĆ(1+I)N

Substitute $12,000 for current cost, 6% for I and 5 for N. Costāofācollegeāināfirstāyear=$12,000(1+0.06)5=$12,000Ć1.338226=$16,058.7

College expense in the first year will be $16,058.7 which will grow 6% annually for next 4 years of college period. Calculation of total cost for all 4 years in spreadsheet, Table (1) Total amount required to meet all college expenses at the beginning is$61,631.23.

Compute future value of current saving.

Given,

Value of saving is $10,000. Interest rate is 9%. Number of years is 5. Formula to calculate future value, Futureāvalueā=CurrentāsavingĆ(1+I)N Here, • I is the interest rate. • N is the number of years. Substitute$10,000 for current saving, 9% for I and 5 for N

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