Question

1.) Renfro Rentals has issued bonds that have a 11% coupon rate, payable semiannually. The bonds mature in 11 years, have a face value of $1,000, and a yield to maturity of 7.5%. What is the price of the bonds? Round your answer to the nearest cent.

2.) To complete your last year in business school and then go through law school, you will need $10,000 per year for 4 years, starting next year (that is, you will need to withdraw the first $10,000 one year from today). Your uncle offers to put you through school, and he will deposit in a bank paying 8.92% interest a sum of money that is sufficient to provide the 4 payments of $10,000 each. His deposit will be made today.

1. How large must the deposit be? Round your answer to the nearest cent.
   $  
   
2. How much will be in the account immediately after you make the first withdrawal? Round your answer to the nearest cent.
   $  
3. How much will be in the account immediately after you make the last withdrawal? Round your answer to the nearest cent. Enter "0" if required

3.) An investment will pay $200 at the end of each of the next 3 years, $300 at the end of Year 4, $600 at the end of Year 5, and $800 at the end of Year 6. If other investments of equal risk earn 7% annually, what is its present value? Round your answer to the nearest cent.
$   

What is its future value? Round your answer to the nearest cent.
$   

4.) You need $17,000 to purchase a used car. Your wealthy uncle is willing to lend you the money as an amortized loan. He would like you to make annual payments for 4 years, with the first payment to be made one year from today. He requires a 5% annual return.

1. What will be your annual loan payments? Round your answer to the nearest cent. Do not round intermediate calculations.
   $
2. 
   
3. How much of your first payment will be applied to interest and to principal repayment? Round your answer to the nearest cent. Do not round intermediate calculations.
   Interest: $
   Principal repayment: $

5.) Bank 1 lends funds at a nominal rate of 8% with payments to be made semiannually. Bank 2 requires payments to be made quarterly. If Bank 2 would like to charge the same effective annual rate as Bank 1, what nominal interest rate will they charge their customers? Round your answer to three decimal places. Do not round intermediate calculations.
%

6.) You own a security with the cash flows shown below.

0

1

2

3

4

0

620

370

260

310

If you require an annual return of 12%, what is the present value of this cash flow stream? Round your answer to the nearest cent. Do not round intermediate calculations.
$

7.) You plan to deposit $2,000 per year for 6 years into a money market account with an annual return of 3%. You plan to make your first deposit one year from today.

1. What amount will be in your account at the end of 6 years? Round your answer to the nearest cent. Do not round intermediate calculations.
   $
2. 
   
3. Assume that your deposits will begin today. What amount will be in your account after 6 years? Round your answer to the nearest cent. Do not round intermediate calculations.
   $

8.) You and your wife are making plans for retirement. You plan on living 25 years after you retire and would like to have $100,000 annually on which to live. Your first withdrawal will be made one year after you retire and you anticipate that your retirement account will earn 10% annually.

1. What amount do you need in your retirement account the day you retire? Round your answer to the nearest cent. Do not round intermediate calculations.
   $
2. 
   
3. Assume that your first withdrawal will be made the day you retire. Under this assumption, what amount do you now need in your retirement account the day you retire? Round your answer to the nearest cent. Do not round intermediate calculations.
   $

Answer 1

Compute the semi-annual coupon using the equation as shown below:

Semi-annual coupon = Annual rate * Face Value / Number of payments in a year

= 11% * $1,000 / 2

= $55

Hence, the semi-annual coupon is $55.

Compute the semi-annual YTM using the equation as shown below:

Semi-annual YTM = Annual YTM / Number of payments in a year

= 7.5% / 2

= 3.75%

Hence, semi-annual YTM is 3.75%.

Compute the period using the equation as shown below:

Period = Years to maturity * Number of payments in a year

= 11 * 2

= 22

Hence, the period is 22.

Compute the Price of the bond using the equation as shown below:

Price = Semi-annual coupon * [{1 - ( 1 + Rate) ^ ( -Period)} / Rate] + [Face Value / ( 1 + Rate) ^ Period]

= $55 * [{( 1 - ( 1 + 3.75%)^(-22)} / 3.75%] + [($1,000 / ( 1 + 3.75%) ^ 22]

= ($55 * 14.80268645) + [($1,000 / ( 1.0375) ^22]

= $1,259.047013

Hence, the price of the bond is $1,259.047013.