part III $(14$ points$)$

A pension fund company is obligated to pay $$300,000$ at the end of year $4$ and $$800,000$ at the end of year $10.$

The company wants to immunize its position. The current market interest rate is $10$ percent per year.

If the pension fund company would like to construct the immunized position using the following two assets:

$3-$year zero coupon bond selling at YTM$=$ market interest rate.

$20-$year $10\%$ coupon bond selling at $YTM=$ market interest rate.

How much money should be placed in each asset?