Question

Question 1. A bank is offering a commercial loan to a company for $10m at an interest rate of 5% APR to be paid off in monthly payments over the next 5 years. a) Find the monthly payments the bank will charge the company as repayment of the loan.

b) Suppose the company is willing to increase its monthly payments at a growth rate of 2% APR (monthly growth rate of 2%/12) in exchange for reducing the loan repayment period. How many months will it take to pay off the $10m loan?

Question 2. The cash prices of six-month and one-year Treasury bills are 94.0 and 89.0 (view the T-bill as zero-coupon bond). A 1.5-year bond that will pay coupons of $4 every six months currently sells for $94.84. A two-year bond that will pay coupons of $5 every six months currently sells for $97.12. Calculate the six-month, one-year, 1.5-year, and two-year zero rates.

Question 3. Consider the zero and forward rates in the table below. Assume that both rates are continuously compounded.

Time-to-maturity (in years) Zero rates (% per annum) Forward rates (% per annum)

1 3.0

2 4.5 X

3 Y 5.8

a) Find the forward rate in the cell labeled X (the forward rate over period [1 year, 2 year]).

b) Find the zero rate in the cell labeled Y (the zero rate of maturity 3 years).

c) A company enters into an FRA that specifies it will receive a fixed rate of 5% (annually compounded) on a principal of $10 million for a one-year period stating in two years. Find the value of the FRA.

Answer 1

(1)

(a)

Total Loan Amount = $ 10 million and Interest Rate = 5% APR or (5/12)% per month

Time period = 5 years or 60 months

Let the monthly repayment be K $

Therefore, the total present value $ K paid for 60 months discounted at (5/12)% per month should be equal to the loan amount, thereby forming 60 period annuity.

10000000 = K x (1/0.004167) x [1 - {1/(1.004167)^(60)}]

K = $ 188714.170

(b) If the Growth Rate =2% APR or 0.1667% per month

This constitutes a growing annuity discounted at the monthly rate of 0.4167 %, with monthly payments starting at $ 188714.170. Let the time period required to pay off the loan be t months.

Therefore, 10000000 = [188714.170 / (0.004167 - 0.001667)] x [1-{1.001667/1.004167}^(t)]

Using the EXCEL Goal Seek Function is used to solve the above equation and get t= 57.01039 months 57 months.

NOTE: Please raise a separate query for solutions to the remaining unrelated questions.