On December ${31}^{st},2013,$ you decided to buy a $40-$year Government of Canada bond. The bond had a

face value of $$100,000.$ The annual coupon rate on the bond was $5\mathrm{.}40\%.$ Coupons were paid semi$-$

annually. On December ${31}^{st},2013,$ the yield to maturity on Government of Canada bonds was $4\mathrm{.}70\%$

per year $($APR compounded semi$-$annually$).$ The term structure of interest rates was flat.

After holding the bond for $10$ years, you decided to sell it on December ${31}^{st},2023.$ Prior to selling

the bond, you received the December ${31}^{st},2023$ coupon payment. On December ${31}^{st},2023,$ the yield

to maturity on Government of Canada bonds had decreased to $3\mathrm{.}30\%$ per year $($APR compounded

semi$-$annually$).$ The term structure of interest rates was flat.

a$)$ How much did you pay for the bond on December $31$ st$,2013?$

b$)$ How much did you sell the bond for on December $31$st$,2023?$

c$)$ What was the effective periodic rate of return that you earned on your investment during the $10$

years?

d$)$ What was the effective annual rate of return that you earned on your investment during the $10$

years?