$3)$ XYZ company has to pay its customers S$2000$ after $2$ years and $$6,000$ after $4$ years.

In order to fund these payments, the company will buy one year and five year zero coupon bonds. The current market interest rate is $10\%.$

The company wants to immunize itself from potential interest rate risk $($Redington Immunization$).$

Find the price of each bond and check that the Redington Immunization conditions are met.