Question

why do we have to put (1.1696) to the power pf 1/4? where does that 1/4 come from in the formula and also why do we bave to use that

(12 Points) You are thinking about purchasing a 4-year zero-coupon bond with a face value of $100. The following information is available from a well-known financial website. • 2-year spot rate is 3% rerum Getring Precenty • Forward rate f2.2 = 5% ZB is geo arruge forward we "B-4-2 Of 2B a. What is the 4-year Spot rate?(24) (tza) * (1 + FA, B-A) B-A = (1HZB) B (1 + Z2)²X (1+82,2)2 = (1+zu)" (1.03) 2x (1.05)2 = (Itzu)" (1.1696)/4= Itzy 0.03995=1+ 2y + zu =. Zu = 3.995), +Z4

Answer 1

(1.03^2)*(1.05^2) = (1+Z4)^4

or, 1.1696 = (1+Z4)^4

taking 1/4th power on both side

we get

1.1696^(1/4) = ((1+Z4)^4)^(1/4)

a mathematics properties says that (M^n)^r = M^(n*r), using same property here we get

1.1696^(1/4) = (1+Z4)^(4*1/4) => 1+Z4 = 1.03995