   Chapter 5, Problem 40P Fundamentals of Financial Manageme...

14th Edition
Eugene F. Brigham + 1 other
ISBN: 9781285867977

Solutions

Chapter
Section Fundamentals of Financial Manageme...

14th Edition
Eugene F. Brigham + 1 other
ISBN: 9781285867977
Textbook Problem

REQUIRED ANNUITY PAYMENTS A father is now planning a saving 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 $15,000, but these costs are expected to increase by 5% annually. The college requires total payment at the start of the year. She now has$7,500 in a college savings account that pays 6% 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 5%) for each year of college and find the total present value of those costs, discounted at 6%, as of the day she enters college. Then find the compounded value of her initial $7,500 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. Annuity: It is an agreement under which a person pays the lump sum payment or number of small transactions and in return, he got the amount at later date or upon annuitization. The purpose of annuity is not to break the flow of income after retirement. Explanation Solution: Compute total cost of college in first year of college. Given, Current cost is$15,000.

Interest rate is 5%.

Number of years is 5.

Formula to calculate cost of first year is,

Costoffirstyear=Currentcost×(1+I)N

Substitute $15,000 for current cost, 5% for I and 5 for N. Costofcollegeinfirstyear=$15,000(1+5%)5=$15,000×1.27=$19,145

College expense in first year will be $19,145 which will grow 5% 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$75,503.12.

Compute future value of current saving.

Given,

Value of saving is \$7500.

Interest rate is 6%.

Number of years is 5.

Formula to calculate future value,

Futurevalue=Currentsaving×(1+I)N

Here,

• I is interest rate

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