Question

Q11 and Q12: You take out a $165,000 loan at a bank with the following terms; Repayment will come in the form of twenty yearly payments of the same amount) with the first being made a year from today. The interest rate is 8%. 11. At the start of the second year, what is the amount of principal still owing? A. $161,800.00 B. $ 151,800.00 C. $161,394.39 D. $165,000.00 12. Find the price of a 6 year (to maturity) bond that makes semi-annual coupon payments of $40 each, has a face value of $1,000 and has a yield to maturity of 6.8%. A. $ 775.21 B. $. 865.71 C. $1,000.00 D. $1,058.32

Answer 1

11.

Compute the PVIFA at 8% and 20 years, using the equation as shown below:

PVIFA = {1 – (1 + Rate)^{-Number of periods}}/ Rate

                   = {1 – (1 + 0.08)^-20}/ 8%

             = 9.81814740671

Hence, the PVIFA at 8% and 20 years is 9.81814740671.

Compute the annual payment of the loan, using the equation as shown below:

Annual payment = Loan value/ PVIFA_{8%, 20 years}

                            = $165,000/ 9.81814740671

                            = $16,805.614457

Hence, the annual payment of the loan is $16,805.614457.   

Compute the loan balance at the start of 2^nd year, using the equation as shown below:

Loan balance = Loan amount + (Loan amount*Rate of interest) – Annual payment

                      = $165,000 + ($165,000*8%) - $16,805.614457

                      = $161,394.39

Hence, the loan balance at the start of 2^nd year is $161,394.39.

12.

Compute the semi-annual discount rate, using the equation as shown below:

Semi-annual rate = Annual rate/ 2

                            = 6.8%/ 2

                            = 3.4%

Hence, the semi-annual rate is 3.4%.

Compute the PVIFA at 3.4% and 12 semi-annual payments, using the equation as shown below:

PVIFA = {1 – (1 + Rate)^{-Number of periods}}/ Rate

                   = {1 – (1 + 0.034)^-12}/ 3.4%

             = 9.72045431848

Hence, the PVIFA at 3.4% and 12 half-years is 9.72045431848.

Compute the PVIF at 3.4% and 12 semi-annual payments, using the equation as shown below:

PVIF = 1/ (1 + Rate)^{Number of periods}

              = 1/ (1 + 0.034)¹²

         = 1/ 1.49364182101

         = 0.66950455312

Hence, the PVIF at 3.4% and 12 half-years is 0.66950455312.

Compute the price of 6 year bond, using the equation as shown below:

Price = (Interest*PVIFA_{3.4%, 12}) + (Face value*PVIF_{3.4%, 12})

         = ($40*9.72045431848) + ($1,000*0.66950455312)

         = $1,058.32

Hence, the price of 6-year bond is $1,058.32.