Time Value of Money
1) Assume that your father is now 50 years old, that he plans to retire in 10 years, and that he expects to live for 25 years after he retires, that is, until he is 85. He wants a ﬁxed retirement income that has the same purchasing power at the time he retires as $40,000 has today (he realizes that the real value of his retirement income will decline year by year after he retires). His retirement income will begin the day he retires, 10 years from today, and he will then get 24 additional annual payments. Inﬂation is expected to be 5 percent per year from today forward; he currently has $100,000 saved up; and he expects to earn a return on his savings of 8 percent per year, annual compounding. To the nearest dollar, how much must he save during each of the next 10 years (with deposits being made at the end of each year) to meet his retirement goal? (Show the time line)
2) A father is planning a savings program to put his daughter through college. His daughter is now 13 and the daughter plans to enroll at the university in 5 years. She would take 4 years to complete her graduation. Currently, the cost of education is $12,500 per year, but a 5 percent annual inflation rate in these cost is forecasted. The daughter recently inherited $7,500 from her grandfather, which the father plans to invest in a bank paying 8 percent interest compound annually, to help meet the cost of the daughter’s education. However, the remaining cost will be met by money, the father will deposit in the savings account. He will make 6 equal deposits to the account, one deposit in each year from now until his daughter starts college. These deposits will begin today and will earn 8 percent interest, compounded annually.
a) What will be the present value of the cost of 4 years of education at the time the daughter becomes 18?
b) What will be the value of the $7,500 that the daughter received from her grandfather’s...
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