An investor gathers the following information about a 3-year, annual-pay bond: • Par value of $1,000 • Coupon of 8% • Current price of $1,100 • 1-year spot interest rate is 5% • 2-year spot interest rate is 6% Using the above information, the 3-year spot rate is closest to: A) 4.37%. B) 4.27%. C) 8.20%.
This kind of question is done by thinking of the bond as three cashflows. $80 at year 1 (discounted at 1.05) $80 at year 2 (discounted at 1.06^2) $1080 at year 3 (discounted at 1.0x^3) Find x. First determine the present value of the first cashflow and second cashflow together. Subtracting this from the present value of the whole bond ($1100) leaves the present value of the third cashflow. Now it’s just algebra ($1080/x^3 = $952.6098) to isolate x and find the answer B.
Its B: Nice explanation NByz 1100=80/(1.05)+80/(1.06)^2+1080/(1+x)^3 solve for x x=4.26% approx
And B is the correct answer. Pretty straight-forward, I guess.