A financial institution has just sold an annuity that calls for a total of $6$ payments of $$300,000.$ The payments will occur every $6$ months for three years. The first payment will occur in $6$ months. The term structure is flat at $3\%$ per year compounded semi$-$annually. The financial institution wants to immunize its obligation by investing the proceeds from the sale of the annuity in a portfolio consisting of $3-$year $4\%$ semi$-$annual coupon bonds and an overnight cash deposit. How much should the financial institution invest in the three year $4\%$ bond?

Question $4$ options:

$898,849$

$888,518$

$1,033,160$

$1,177,802$

$981,502$