Demonstrate through an example $($create it$)$ that a liability with a single cash flow that matures in $10$ years can be immunized against interest rate risk if funded with a single bond with the same duration. Demonstrate that value of the proceedings from the sale of this bond in $t=10$ with the accrued value of the re$-$invested coupons until $t=10($time when the liability must be paid$)$ are close enough to the value needed to meet the obligation in $t=10.$ Simulate the value of these proceedings $($reinvestment of coupons plus value from the bond sale$)$ using different YTM for this bond $($at least one change up and one change down$),$ demonstrating that independently of the YTM levels on this bond, the sum of the re$-$invested coupons until $t=10$ plus the proceedings from its sale in $t=10$ will be always around the value of the liability, immunizing the portfolio.