Question $4$: Answer the following questions. $(2$ marks$)$

i$)$ A zero$-$coupon bond with a par value of $$5,000$ matures in $10$ years. At what price would this bond provide a yield to maturity that matches the current market rate of $6$ percent?

ii$)$ What happens to the price of this bond if interest rates fall to $5$ percent?

iii$)$ Given the above changes in the price of the bond and the interest rate, calculate the bond pric elasticity.