In mid$-$September $2024$ the yield on ten$-$year government bonds issued by the Australian government was $3\mathrm{.}8$ per cent. In mid$-$November $2024$ the yield was $4\mathrm{.}7$ per cent $($source: tradingeconomics.com$).$ Predict the effect of these changes in yield on the price of the ten$-$year government bonds. To answer this question you could consider a ten$-$year bond issued in September $2024$ with principal value A$$1,000$ and yield $3\mathrm{.}8\%.$ It pays annual coupons of A$$38$ each. On redemption there is a total payment of A$$1,038($the repayment of A$$1,000$ principal plus the final A$$38$ coupon$).$ Calculate the modified duration and convexity, and predict the change in bond price if yields increase from $3\mathrm{.}8\%$ by $90$ basis points $($plus $0\mathrm{.}9\%).$ You might also choose to compare these predictions to the actual change in bond price for a yield of $4\mathrm{.}7\%.$ Make sure you explain what you are doing, provide interpretation of the results, and comment on your findings. In your calculations keep time to maturity at $10$ years.