You are looking to invest $$200,000.$ You have $3$ possible investment options: $($I$)$ A lump sum of $$600,000$ payable in $10$ years

$($II$)$ A $$200,000$ par$-$value $5-$year bond with semi$-$annual coupons at j$2=13\mathrm{.}6\%.$

$($III$)$ A perpetuity paying $$23,000$ at the end of every year.

Using the net present value method of business decision making, which option should be chosen, if any, if the cost of capital is j$2=10\%?$