Calculate the price of a 5% coupon, $1000 face value 5 year bond that's callable after one year for $1030 if there's an equal chance that interest rates for each of the next five years will be 4%, 5% or 6% (in all cases, rates will be constant for all five years so either 4%, 4%, 4%, 4%, 4% or 5%, 5%, 5%, 5%, 5% or 6%, 6%, 6%, 6%, 6%).Assume the call provision can only be exercised after the first coupon is paid (at the so called coupon anniversary).If the probability that both 4% and 6% falls to 10% (leaving the average rate the same: 5%), the price of this bond will rise.Intuitively, explain why? Please show all work.