You just started your first job

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FUTURE VALUE

You just started your first job, and you want to buy a house within 3 years. You are currently saving for the down payment. You plan to save $5,000 the first year. You also anticipate that the amount you save each year will rise by 10 percent a year as your salary increases over time. Interest rates are assumed to be 7 percent, and all savings occur at year end.

HOW MUCH MONEY WILL YOU HAVE FOR A DOWN PAYMENT IN 3 YEARS?

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REQUIRED ANNUITY PAYMENTS

A 15-year security has a price of $340.4689. The security pays $50 at the end of each of the next 5 years, and then it pays a different fixed cash flow amount at the end of each of the following 10 years. Interest rates are 9 percent.

WHAT IS THE ANNUAL CASH FLOW AMOUNT BETWEEN YEARS 6 AND 15?

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FUTURE VALUE OF AN ANNUITY

Erika and Katherine have both been given $30,000 by their grandparents today on their 25thbirthdays. They want to save for their future and have aspirations of one day being millionaires. Each woman plans to make annual contributions on her birthday, beginning next year. Erika and Katherine have each opened investment accounts at the First National Bank and Second National Bank, respectively, and they expect to earn nominal returns of 8 and 9 percent, respectively. Erika has already decided to deposit $5,000 each year into her investment account, while Katherine is unsure of the amount she will deposit annually.
(a.) How long will it take Erika before she reaches her investment goal of $1 million?
(b.) If Katherine decides to make the same annual contributions as Erika, how much sooner would she reach the investment goal?
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EXPECTED RATE OF RETURN

A 5-year security has a price of $1,300. The security pays $400 at the end of each of the next 5 years.

WHAT IS THE EXPECTED RETURN OF THIS INVESTMENT TO THAT INVESTOR?

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REQUIRED ANNUITY PAYMENTS

A father is planning a savings program to put his daughter through college. His daughter is now 13 years old. She plans to enroll at the university in 5 years, and it should take her 4 years to complete her education. Currently, the cost per year (for everything—food, clothing, tuition, books, transportation, and so forth) is $12,500, but a 5 percent annual inflation rate in these costs is forecasted. The daughter recently received $7,500 from her grandfather’s estate; this money, which is invested in a bank account paying 8 percent interest, compounded annually, will be used to help meet the costs of the daughter’s education. The remaining costs 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 also 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? [Hint: Calculate the future value of the cost (at 5%) for each year of her education, then discount 3 of these costs back (at 8%) to the year in which she turns 18, then sum the 4 costs.]
b. What will be the value of the $7,500 that the daughter received from her grandfather’s estate when she starts college at age 18? [Hint: Compound for 5 years at an 8 percent annual rate.]
c. If the father is planning to make the first of 6 deposits today, how large must each deposit be for him to be able to put his daughter through college? [Hint: An annuity due assumes interest is earned on all deposits; however, the 6th deposit earns no interest—therefore, the deposits are an ordinary annuity.]

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