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[solution]: MBA536 Homework 3 1-Carol Calc plans on retiring on her 60 th

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MBA536 Homework 3

1-Carol Calc plans on retiring on her 60^{th} birthday. She wants to put the same amount of funds aside each year for the next twenty years ? starting next year ? so that she will be able to withdraw $50,000 per year for twenty years once she retires, with the first withdrawal on her 61^{st} birthday. Carol is 20 years old today. How much must she set aside each year for her retirement if she can earn 10% on her funds?

2-Have I got a deal for you! If you lend me $100,000 today, I promise to pay you back in twenty-five annual installments of $5,000, starting five years from today (that is, my first payment to you is five years from today). You can earn 6% on your investments. Will you lend me the money?

3-The Trust Worthy loan company is willing to lend you $10,000 today if you promise to repay the loan in six monthly payments of $2,000 each, beginning today. What is the effective annual interest rate on Trust Worthy's loan terms?

4- A company wants to provide a retirement plan for an employee who is aged 55 now. The plan will provide her with an annuity immediate of $7,000 every year for 15 years upon her retirement at the age of 65. The company is funding this plan with an annuity-due of 10years. If the rate of interest is 5%, what is the amount of installment the

company should pay?

5- Find the present value of an annuity-immediate of $100 per quarter for 4 years, if interest is compounded semiannually at the nominal rate of 6%.

6- For each of the following five situations, find the present value of the ordinary annuity described.

1. $2000 per month for 5 years at a rate of 6% compounded monthly.

2. $5500 per quarter for 6 ½ years at 5.6% compounded quarterly.

3. $150 per month for 3 years at 8% compounded semi-annually.

4. Joe wants to invest a lump sum of money now to cover a monthly commitment

of $100 over 5 years. If the lump sum is invested at 7.5% compounded monthly,

what amount will Joe invest?

5. Jane?s car insurance company charges a monthly premium of $41.50. What is

the present value of two year?s premiums if the rate of inflation is 0.3% per

month?

7- Mrs. Carter deposits $100 in the bank at the end of each month. If the bank pays 7% per year compounder continuously, how much money will she have accumulated at the end of 5 years. {hint: This is a mixed problem regarding monthly payments and continuous compounding. Give it a shot and email me if you are stuck. There is a simple equation for this}

MBA536 Homework 3

1-Carol Calc plans on retiring on her 60th birthday. She wants to put the same amount of

funds aside each year for the next twenty years ? starting next year ? so that she will be

able to withdraw $50,000 per year for twenty years once she retires, with the first

withdrawal on her 61st birthday. Carol is 20 years old today. How much must she set aside

each year for her retirement if she can earn 10% on her funds?

2-Have I got a deal for you! If you lend me $100,000 today, I promise to pay you back in

twenty-five annual installments of $5,000, starting five years from today (that is, my first

payment to you is five years from today). You can earn 6% on your investments. Will you

lend me the money?

3-The Trust Worthy loan company is willing to lend you $10,000 today if you promise to

repay the loan in six monthly payments of $2,000 each, beginning today. What is the

effective annual interest rate on Trust Worthy's loan terms?

4- A company wants to provide a retirement plan for an employee who is aged 55 now.

The plan will provide her with an annuity immediate of $7,000 every year for 15 years

upon her retirement at the age of 65. The company is funding this plan with an annuitydue of 10years. If the rate of interest is 5%, what is the amount of installment the

company should pay?

5- Find the present value of an annuity-immediate of $100 per quarter for 4 years, if

interest is compounded semiannually at the nominal rate of 6%.

6- For each of the following five situations, find the present value of the ordinary

annuity described.

1. $2000 per month for 5 years at a rate of 6% compounded monthly.

2. $5500 per quarter for 6 ½ years at 5.6% compounded quarterly.

3. $150 per month for 3 years at 8% compounded semi-annually.

4. Joe wants to invest a lump sum of money now to cover a monthly commitment

of $100 over 5 years. If the lump sum is invested at 7.5% compounded monthly,

what amount will Joe invest?

5. Jane?s car insurance company charges a monthly premium of $41.50. What is

the present value of two year?s premiums if the rate of inflation is 0.3% per

month?

7- Mrs. Carter deposits $100 in the bank at the end of each month. If the bank pays 7%

per year compounder continuously, how much money will she have accumulated at the

end of 5 years. {hint: This is a mixed problem regarding monthly payments and

continuous compounding. Give it a shot and email me if you are stuck. There is a simple

equation for this}

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