Question

1a) Suppose the 1-year effective annual interest rate is 4.9% and the 2-year effective rate is 6.5%. Compute the fixed rate in a 2-year amortizing interest rate swap based on $460,000 of notional principal in the first year and $390,000 in the second year.

Answers: a. 5.67% b. 6.62% c. 6.32% d. 5.60% e. 6.45%

1b)

Suppose that 1-year, 2-year, and 3-year forward prices for the British pound are $1.76/£, $1.67/£, and $1.37/£, respectively. The 1-year, 2-year, and 3-year effective annual interest rates in the U.S. are 5.3%, 4.9%, and 4.7%. What is the fixed exchange rate in a 3-year British pound swap? (In other words, what 3-year U.S. dollar annuity is equivalent to a 3-year annuity of £1?)

Answers: a. $1.97 b. $1.80 c. $1.46 d. $1.61 e. $1.86

Please provide proper explanation and formulas. Thank you!

Answer 1

EAR for 1st year = 4.9%,

Interest rate for year 1 = 5.8%

EAR for 2nd year = 6.5%

Interest rate for 2 year = [(1+6.5%)² / (1+4.9%)] - 1

= [(1.065)²/(1.049)¹]-1 = 0.0812 or 8.12%

Interest paid for first year = 4.9% * 460000 = 22540

Interest paid for 2nd year = 390000 * 8.12% = 31,668

Since its a swap:

R : the present value of interest on variable rate = present value of interest at fixed rate

=(4.9%*460000/1.049)+ (8.12%*390000/1.065²) = (R*460000/1.049)+ (R*390000/1.065²)

=21487.13+27920.39 = 438512R+343847R

=49407.52 =782360R

R = 0.063152 or 6.32%

Hence correct answer is option "c"