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##### Financial Planning Problems

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Question;4-21. When you purchased your;house, you took out a 30-year annual-payment mortgage with an;interest rate of 6% per year. The;annual payment on the mortgage is $12,000. You have just;made a payment and have now;decided to pay the mortgage off by repaying the outstanding;balance. What is the payoff amount;if;a. You have lived in the house for;12 years (so there are 18 years left on the mortgage)?;b. You have lived in the house for;20 years (so there are 10 years left on the mortgage)?;c. You have lived in the house for;12 years (so there are 18 years left on the mortgage) and you;decide to pay off the mortgage;immediatelybefore;the twelfth payment is due?;=;4-22. You are 25 years old and;decide to start saving for your retirement. You plan to save $5000 at;the end of each year (so the first;deposit will be one year from now), and will make the last;deposit when you retire at age 65.;Suppose you earn 8% per year on your retirement savings.;a. How much will you have saved;for retirement?;b. How much will you have saved if;you wait until age 35 to start saving (again, with your first;deposit at the end of the year)?;4-23. Your grandmother has been;putting $1000 into a savings account on every birthday since your;first (that is, when you turned;1). The account pays an interest rate of 3%. How much money will;be in the account on your 18th;birthday immediately after your grandmother makes the deposit;on that birthday?;4-24. A rich relative has;bequeathed you a growing perpetuity. The first payment will occur in a year;and will be $1000. Each year after;that, you will receive a payment on the anniversary of the last;payment that is 8% larger than the;last payment. This pattern of payments will go on forever. If;the interest rate is 12% per year;a. What is today?s value of the;bequest?;b. What is the value of the;bequest immediately after the first payment is made?;4-25. You are thinking of building;a new machine that will save you $1000 in the first year. The;machine will then begin to wear;out so that the savingsdeclineat a rate of 2% per year forever.;What is the present value of the;savings if the interest rate is 5% per year?;4-26. You work for a;pharmaceutical company that has developed a new drug. The patent on the drug;will last 17 years. You expect;that the drug?s profits will be $2 million in its first year and that;this amount will grow at a rate of;5% per year for the next 17 years. Once the patent expires;other pharmaceutical companies;will be able to produce the same drug and competition will;likely drive profits to zero. What;is the present value of the new drug if the interest rate is 10%;per year?;4-27. Your oldest daughter is;about to start kindergarten at a private school. Tuition is $10,000 per;year, payable at thebeginningof the school year. You expect to;keep your daughter in private;school through high school. You;expect tuition to increase at a rate of 5% per year over the 13;years of her schooling. What is;the present value of the tuition payments if the interest rate is 5%;per year? How much would you need;to have in the bank now to fund all 13 years of tuition?;4-28. A rich aunt has promised you;$5000 one year from today. In addition, each year after that, she;has promised you a payment (on the;anniversary of the last payment) that is 5% larger than the;last payment. She will continue to;show this generosity for 20 years, giving a total of 20;payments. If the interest rate is;5%, what is her promise worth today?;4-29. You are running a hot;Internet company. Analysts predict that its earnings will grow at 30% per;year for the next five years.;After that, as competition increases, earnings growth is expected to;slow to 2% per year and continue;at that level forever. Your company has just announced;earnings of $1,000,000. What is;the present value of all future earnings if the interest rate is 8%?;(Assume all cash flows occur at;the end of the year.).;4-30. Your brother has offered to;give you $100, starting next year, and after that growing at 3% for;the next 20 years. You would like;to calculate the value of this offer by calculating how much;money you would need to deposit in;the local bank so that the account will generate the same;cash flows as he is offering you.;Your local bank will guarantee a 6% annual interest rate so long;as you have money in the account.;a. How much money will you need to;deposit into the account today?;b. Using an Excel spreadsheet;show explicitly that you can deposit this amount of money into;the account, and every year;withdraw what your brother has promised, leaving the account;with nothing after the last;withdrawal.;4-31. You have decided to buy a;perpetuity. The bond makes one payment at the end of every year;forever and has an interest rate;of 5%. If you initially put $1000 into the bond, what is the;payment every year?;4-32. You are thinking of;purchasing a house. The house costs $350,000. You have $50,000 in cash that;you can use as a down payment on;the house, but you need to borrow the rest of the purchase;price. The bank is offering a;30-year mortgage that requires annual payments and has an;interest rate of 7% per year. What;will your annual payment be if you sign up for this mortgage?;4-33. You are thinking about;buying a piece of art that costs $50,000. The art dealer is proposing the;following deal: He will lend you;the money, and you will repay the loan by making the same;payment every two years for the;next 20 years (i.e., a total of 10 payments). If the interest rate is;4%, how much will you have to pay;every two years?;4-34. You would like to buy the;house and take the mortgage described in Problem 32. You can afford;to pay only $23,500 per year. The;bank agrees to allow you to pay this amount each year, yet still;borrow $300,000. At the end of the;mortgage (in 30 years), you must make aballoonpayment;that is, you must repay the;remaining balance on the mortgage. How much will this balloon;payment be?;4-35. You are saving for;retirement. To live comfortably, you decide you will need to save $2 million;by the time you are 65. Today is;your 30th birthday, and you decide, starting today and;continuing on every birthday up to;and including your 65th birthday, that you will put the same;amount into a savings account. If;the interest rate is 5%, how much must you set aside each year;to make sure that you will have $2;million in the account on your 65th birthday?

Paper#50996 | Written in 18-Jul-2015

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