You are looking to invest $$200,000.$ You have $3$ possible investment options:

$($I$)$ A lump sum of $$640,000$ payable in $10$ years

$($II$)$ An annuity paying $$30,000$ at the end of every years for $15$ years

$($III$)$ A perpetuity paying $$25,000$ 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$1=12\%?$