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Bob invested $2,000 in an investment fund on his 21st birthday.

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Bob invested $2,000 in an investment fund on his 21st birthday. The fund pays 7% interest compounded semiannually. Bob is celebrating his 50th birthday today. Bob decides he wants to retire on his 60th birthday and he wants to withdraw $75,000 per year, the first withdrawal on his 60th birthday and the last withdrawal on his 90th birthday. Bob expects to receive $100,000 from his employer on his 55th birthday in recognition of his long service to the company.

Assume Bob has not taken any money out of his investment fund since he initially funded it on his 21st birthday, and that he will deposit the $100,000 from his employer into the investment fund on his 55th birthday. The investment fund will be used to pay for Bob’s retirement.

a) If Bob makes no additional deposits into his investment fund, how much will be available for retirement at age 60?

b) Since the amount in (a) is insufficient to meet his retirement goals, Bob decides to deposit equal annual amounts into the investment fund beginning on his 51st birthday and ending on his 59th birthday, so that he can meet his retirement goals. How much will each deposit be?

Sunrise Industries wishes to accumulate funds to provide a retirement

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Sunrise Industries wishes to accumulate funds to provide a retirement annuity for its vice president of research, Jill Moran. Ms Moran, by contract, will retire at the end of exactly 12 yrs. Upon retirement, she is entitled to receive an annual end of year payment of $42,000 for exactly 20 years. If she dies prior to the end of the 20 year period the annual payments will pass to her heirs. During the 12 year accumulation period, Sunrise wishes to fund the annuity by making equal, annual, end of year deposits into an account earning 9% interest. Once the 20 year distribution period begins, sunrise plans to move the accumulated monies into an account earning a garunteed 12% per year. At the end of the distribution period the account balance will equal zero. Note that the first deposit will be made at the end of year 1 and that the first distribution payment will be received at the end of year 13.

A. Draw a timeline depicting all of the cash flows associated with Sunrise view of the retirement annuity.

B. How large a sum must Sunrise accumulate by the end of year 12 to provide the 20 year, $42,000 annuity?

C. How large must Sunrise’s equal, annual, end of year deposits into the account be over the 12 year accumulation period to fund fully Ms Morgans retirement annuity?

D. How much would Sunrise have to deposit annually during the accumulation period if it could earn 10% rather than 9% during the accumulation period?

E. How much would Sunrise have to deposit annually during the accumulation period if Ms Morgan’s retirement annuity were a perpetuity and all other terms were the same as initially described?

Problems 5-9, 5-10, 5-11, 5-12, 5-14, 5-15

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Problems 5-9, 5-10, 5-11, 5-12, 5-14, 5-15

5-9. Present and future values for different periods

Find the following values using the equations and then a financial calculator. Compounding/discounting occurs annually
a. An initial $500 compounded for 1 year at 6%
b. An initial $500 compounded for 2 years at 6%
c. The present value of $500 due in 1 year at a discount rate of 6%
d. The present value of $500 due in 2 years at a discount rate of 6%

5-10. Present and future values for different interest rates

Find the following value. Compounding/discounting occurs annually
a. An initial $500 compounded for 10 years at 6%
b. An initial $500 compounded for 10 years at 12%
c. The present value of $500 due in 10 years at 6%
d. The present value of $1,552.90 due in 10 years at 12% and at 6%
e. Define present value and illustrate it using a time line with data from Part d. How are present values affected by interest rates?

5-11. Growth rates
shalit Corporation’s 2008 sales were $12million. Its 2003 sales were $6 million
a. At what rate have sales been growing?
b. B. Supposed someone made this statement: “Sales doubled in 5 years. This presents a growth of 100% in 5 years; so dividing 100% by 5, we find the growth rate to be 20% per year.” Is that statement correct?

5-12. Effective rate of interest
Find the interest rates earned on each of the following:

a. You borrow $700 and promise to pay back $749 at the end of 1 year.
b. You lend $700 and the borrower promises to pay you $749 at the end of 1 year
c. You bowwow $85,000 and promise to make payment of $201,229 at the end of 10 years
d. You borrow $9,000 and promise to make payments of $2,684.80 at the end of each for 5 years.

5-14. Future value of an annuity
Find the future values of these ordinary annuities. Compounding occurs once a year.
a. $400 per year for 10 years at 10%
b. $200 per year for 5 years at 5%
c. $400 per year for 5 years at 0%
d. Rework Parts a, b, and c assuming they are annuities due.

5-15. Present value of an annuity
Find the present values of these ordinary annuities. Discounting occurs once a year.
a. $400 per year for 10 years at 10%
b. $200 per year for 5 years at 5%
c. $400 per year for 5 years at 0%
d. Rework Parts a, b, and c assuming they are annuities due.

Carrie Tune will receive $19,500 a year for the next 20 years

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1. Carrie Tune will receive $19,500 a year for the next 20 years as a result of the new song she has written. If a 10 percent rate is applied, should she be willing to sell out her future rights now for $160,000?

2. At a growth (interest) rate of 8 percent annually, how long will it take for a sum to double? To triple? Select the year that is closest to the correct answer.

3. If you owe $30,000 payable at the end of five years, what amount should your creditor accept in payment immediately if she could earn 11 percent on her money?

4. Mr Flint retired as president of the Color Tile Company but is currently on a consulting contract for $45,000 per year for the next 10 years.

a. If Mr. Flint’s opportunity cost (potential return) is 10 percent, what is the present value of his consulting contract?

b. Assuming that Mr. Flint will not retire for two more years and will not start to receive his 10 payments until he end of the third year, what would be the value of his deferred annuity?

5. Cousin Bertha invested $100,000 10 years ago at 12 percent, compounded quarterly. How much has she accumulated?

As stated in the chapter, annuity payments are assumed to come at the end

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1. As stated in the chapter, annuity payments are assumed to come at the end of each payment period (termed an ordinary annuity). However, an exception occurs when the annuity payments come in the beginning of each period (termed an annuity due). To find the present value of an annuity due, subtract 1 from n an add 1 to the tabular value. For example, to find the future future percent, go to Appendix C for n = 6 and i = 10 percent. Look up the value of 7.716 and subtract 1 from it for an answer of 6.716 or $671.60 ($100 x 6.716).

What is the future value of a 10-year annuity of $2,000 per period where payments come at the beginning of each period? The interest rate is 8 percent.

2. Related to the discussion in problem 23, what is the percent value of a 10-year annuity of $3,000 per period in which payments come at the beginning of each period? The interest rate is 12 percent.

3. You need $23,956 at the end of nine year, and your only investment outlet is a 7 percent long-term certificate of deposit (compounded annually). With the certificate of deposit, you make an initial investment at the beginning of the first year.

a. What single payment could be made at the beginning of the first year to achieve this object?
b. What amount could you pay ay the end of each year annually for nine years to achieve this same objective?

4. Beverly Hills started a paper route on January 1, 2001. Every three months, she deposits $300 in her bank account, which earns 8 percent annually but is compounded quarterly. On December 31, 2004, she used the entire balance in her bank account to invest in an investment at 12 percent annually. How much will she have on December 31, 2007?

5. On January 1, 2005, Mr. Dow bought 100 shares of stock at $12 per share. On December 31, 2008, he sold the stock for $18 per share. What is his annual rate on return? Interpolate to find the answer.

6. C. D. Rom has just given an insurance company $30,000. In return, he will receive an annuity of $3,200 for 20 years.

At what rate of return must the insurance company invest this $30,000 in order to make the annual payments? Interpolate.

7. Rusty Steele will receive the following payments at the end of the next three years: $4,00. $7,000, and $9,000. Then from the end of the fourth year through the end of the tenth year, he will receive an annuity of $10,000. At a discount rate of 10 percent, what is the present value of all future benefits?

General Mills will receive $27,500 a year for the next 10 years

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1. General Mills will receive $27,500 a year for the next 10 years as a payment for a weapon he invented. If a 12 percent rate is applied, should he be willing to sell out his future rights now for $160,000?

2. Determine the amount of money in a saving account at the end of five years, given an initial deposit of $3, 000 and an 8 percent annual interest rate when interest is compounded (a) annually, (b) semiannually, and (c) quarterly.

3.Kelly Greene has a contract in which she will receive the following payments for the next five years: $3,000, $4,000, $5,000, $6,000, and $7,000. She will then receive an annuity of $9,000 a year from the end of sixth through the end of the 15th year. The appropriate discount rate is 13 percent. If she is offered $40,000 to cancel the contract, should she do it?

4. Kay Mart has purchased an annuity to begin payment at the end of 2009 (the date of the first payment). Assume it is now the beginning of 2007. The annuity is for $12,000 per year and is designed to last eight years.
If the discount rate for the calculation is 11 percent, what is the most she should have paid for the annuity?

5. If you borrow $9,725 and are required to pay back the loan in five equal annual installments of $2,500, what is the interest rate associated with the loan?

You will receive $4,000, three years from now.

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1. You will receive $4,000, three years from now. The discount rate is 10 percent.

a. What is the value of your investment two years from now? Multiply $4,000 X .909 (one year’s discount rate at 10 percent).

b. What is the value of your investment one year from now? Multiply your answer to part a by .909 (one year’s discount rate at 10 percent).

c. What is the value of your investment today? Multiply your answer to part b by .909 (one year’s discount rate at 10 percent).