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Question;6-26;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?;6-27;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?;6-29;FUTURE VALUE OF AN ANNUITY;Erika;and Katherine have both been given $30,000 by their grandparents today on;their 25th birthdays. 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?;6-33;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?;6-48;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.]

 

Paper#51225 | Written in 18-Jul-2015

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