Step by Step Assistance

Sunday, 10 March 2013

You are planning to retire in 14 years and would like to invest all your current savings in bonds issued by your state. The bonds have the face value of $5,000, annual coupon rate of 3.8 percent, and maturity of 26 years. The bonds are currently priced to yield 5.3 percent.

You are planning to retire in 14 years and would like to invest all your current savings in bonds issued by your state. The bonds have the face value of $5,000, annual coupon rate of 3.8 percent, and maturity of 26 years. The bonds are currently priced to yield 5.3 percent.
You expect to be able to reinvest the semiannual coupon payments you will receive over your investment horizon at the annual rate of 4.4 percent. You also expect that the annual yield for comparable bonds at the time you plan to sell your bonds in 14 years (end of your investment horizon) will be 4.9 percent.
 
What is the expected annual realized compound yield of these bonds? (Do not round intermediate calculations and round your final answers to 3 decimal places. (e.g., 32.167))


 Total return  %
Suppose the real rate is 4.0 percent and the inflation rate is 5.6 percent.
  
What rate would you expect to see on a Treasury bill? (Round your answer to 2 decimal places. (e.g., 32.16))

  Treasury bill rate %  


Explanation:

You’ve just joined the investment banking firm of Dewey, Cheatum, and Howe. They’ve offered you

You’ve just joined the investment banking firm of Dewey, Cheatum, and Howe. They’ve offered you two different salary arrangements. You can have $83,000 per year for the next two years, or you can have $72,000 per year for the next two years, along with a $28,000 signing bonus today. The bonus is paid immediately, and the salary is paid in equal amounts at the end of each month.
  
If the interest rate is 8 percent compounded monthly, what is the PV for both the options? (Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16))
   
  PV
  Option 1 $  
  Option 2 $  


rev: 08_21_2012


Explanation:

You have 34 years left until retirement and want to retire with $3.6 million. Your salary is paid

You have 34 years left until retirement and want to retire with $3.6 million. Your salary is paid annually, and you will receive $52,000 at the end of the current year. Your salary will increase at 2.2 percent per year, and you can earn a 15.2 percent return on the money you invest. If you save a constant percentage of your salary, what percentage of your salary must you save each year? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
 
  Percent of salary to save %  


Explanation:
We need to find the lump sum payment into the retirement account. The present value of the desired amount at retirement is:
   
PV = FV/(1 + r)t
PV = $3,600,000/(1 + 0.152)34
PV = $29,303.41
    
This is the value today. Since the savings are in the form of a growing annuity, we can use the growing annuity equation and solve for the payment. Doing so, we get:
   
PV = C {[1 – ((1 + g)/(1 + r))t ] / (rg)}
$29,303.41 = C{[1 – ((1 + 0.022)/(1 + 0.152))34 ] / (0.152 – 0.022)}
C = $3,875.56
  
This is the amount you need to save next year. So, the percentage of your salary is:
  
Percentage of salary = $3,875.56/$52,000
Percentage of salary = 0.0745, or 7.45%
 
Note that this is the percentage of your salary you must save each year. Since your salary is increasing at 2.2 percent, and the savings are increasing at 2.2 percent, the percentage of salary will remain constant.

You have just arranged for a $1,620,000 mortgage to finance the purchase of a large tract of land. The

You have just arranged for a $1,620,000 mortgage to finance the purchase of a large tract of land. The mortgage has an APR of 6.2 percent, and it calls for monthly payments over the next 22 years. However, the loan has an eight-year balloon payment, meaning that the loan must be paid off then.
 
How big will the balloon payment be? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
 
  Balloon payment $  


Explanation:

An insurance company is offering a new policy to its customers. Typically, the policy is bought by a

An insurance company is offering a new policy to its customers. Typically, the policy is bought by a parent or grandparent for a child at the child’s birth. The details of the policy are as follows: The purchaser (say, the parent) makes the following six payments to the insurance company:
 
       
  First birthday: $ 790  
  Second birthday: $ 790  
  Third birthday: $ 890  
  Fourth birthday: $ 850  
  Fifth birthday: $ 990  
  Sixth birthday: $ 950  

 
After the child’s sixth birthday, no more payments are made. When the child reaches age 65, he or she receives $290,000. The relevant interest rate is 10 percent for the first six years and 7 percent for all subsequent years.

Find the future value of the payment at the child's 65th birthday. (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
 
  Future value $  



Explanation:

Prepare an amortization schedule for a five-year loan of $60,000. The interest rate is 9 percent per

Prepare an amortization schedule for a five-year loan of $60,000. The interest rate is 9 percent per year, and the loan calls for equal annual payments. (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
 
Year Beginning
Balance
Total
Payment
Interest
Payment
Principal
Payment
Ending
Balance
1 $ $ $ $ $  
2  
3  
4  
5  

 
How much interest is paid in the third year? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
 
  Interest paid $  

The interest rate is 9 percent per year, and the loan calls for equal annual payments. How much total interest is paid over the life of the loan? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
 
  Total interest paid $  


Explanation:
The payment for a loan repaid with equal payments is the annuity payment with the loan value as the PV of the annuity. So, the loan payment will be:
   
PVA = $60,000 = C {[1 – 1 / (1 + 0.09)5] / 0.09}
C = $15,425.55
  
The interest payment is the beginning balance times the interest rate for the period, and the principal payment is the total payment minus the interest payment. The ending balance is the beginning balance minus the principal payment. The ending balance for a period is the beginning balance for the next period.
 
In the third year, $3,514.19 of interest is paid.
 
Total interest over life of the loan = $5,400 + 4,497.70 + 3,514.19 + 2,442.17 + 1,273.67
Total interest over life of the loan = $17,127.74

A 15-year annuity pays $1,900 per month, and payments are made at the end of each month. If the

A 15-year annuity pays $1,900 per month, and payments are made at the end of each month. If the interest rate is 10 percent compounded monthly for the first seven years, and 6 percent compounded monthly thereafter, what is the present value of the annuity? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
 
  Present value $  


Explanation:

What is the value today of $5,000 per year, at a discount rate of 9 percent, if the first payment is

What is the value today of $5,000 per year, at a discount rate of 9 percent, if the first payment is received 5 years from today and the last payment is received 15 years from today? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
 
  Value today $  


Explanation:
 

The present value of the following cash flow stream is $8,550 when discounted at 9.3 percent

The present value of the following cash flow stream is $8,550 when discounted at 9.3 percent annually. What is the value of the missing cash flow? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
  
Year   Cash Flow
  1     $ 2,150  
  2        
  3       2,750  
  4       3,350  



Explanation: