Suppose a bank holds a $$100,000$ face value bond, with $4\%$ coupon that pays

semiannually with $5$ years to maturity.

a$)$ What is the price of the bond if market interest rates are $4\%?$

b$)$ What is the price of the bond $2$ years from now, with $3$ years left to maturity. Again

assume that market interest rates are $4\%.$

c$)$ What is the price of the bond $2$ years from now with $3$ years left to maturity, but

market interest rates are $6\%?$

d$)$ What is gain$/$loss from market interest rates going up from $4\%$ in case $($b$)$ to $6\%$ in

case $($c$)?$

e$)$ What is the bond $2$ years from now with $3$ years left to maturity, but market interest

rates are $2\%?$

f$)$ What is gain$/$loss from market interest rates going down from $4\%$ in case $($b$)$ to $2\%$ in

case $($e$)?$