An investor borrows an amount at an annual effective rate of $5\%,$ and will repay all interest and principal in a lump sum at the end of $10$ years. She uses the amount borrowed to

purchase a $1,000$ par value $10-$year bond with $8\%$ semi$-$annual coupons bought to yield

$6\%$ convertible semi$-$annually. As each coupon is received, it is immediately reinvested

at a nominal rate of $4\%$ convertible semi$-$annually.

Calculate the net gain to the investor at the end of $10$ years after the loan is repaid.