Project $1$ requires an original investment of $$43,000.$ The project will yield cash flows of $$12,000$ per year for $5$ years. Project $2$ has a computed net present value of $$10,500$ over a $3-$year life. Project $1$ could be sold at the end of $3$ years for a price of $$47,000.$Use the Present Value of $$1$ at Compound Interest and the Present Value of an Annuity of $$1$ at Compound Interest tables shown below.Present Value of $$1$ at Compound InterestYear$6\%10\%12\%15\%20\%10\mathrm{.}9430\mathrm{.}9090\mathrm{.}8930\mathrm{.}8700\mathrm{.}83320\mathrm{.}8900\mathrm{.}8260\mathrm{.}7970\mathrm{.}7560\mathrm{.}69430\mathrm{.}8400\mathrm{.}7510\mathrm{.}7120\mathrm{.}6580\mathrm{.}57940\mathrm{.}7920\mathrm{.}6830\mathrm{.}6360\mathrm{.}5720\mathrm{.}48250\mathrm{.}7470\mathrm{.}6210\mathrm{.}5670\mathrm{.}4970\mathrm{.}40260\mathrm{.}7050\mathrm{.}5640\mathrm{.}5070\mathrm{.}4320\mathrm{.}33570\mathrm{.}6650\mathrm{.}5130\mathrm{.}4520\mathrm{.}3760\mathrm{.}27980\mathrm{.}6270\mathrm{.}4670\mathrm{.}4040\mathrm{.}3270\mathrm{.}23390\mathrm{.}5920\mathrm{.}4240\mathrm{.}3610\mathrm{.}2840\mathrm{.}194100\mathrm{.}5580\mathrm{.}3860\mathrm{.}3220\mathrm{.}2470\mathrm{.}162$Present Value of an Annuity of $$1$ at Compound InterestYear$6\%10\%12\%15\%20\%10\mathrm{.}9430\mathrm{.}9090\mathrm{.}8930\mathrm{.}8700\mathrm{.}83321\mathrm{.}8331\mathrm{.}7361\mathrm{.}6901\mathrm{.}6261\mathrm{.}52832\mathrm{.}6732\mathrm{.}4872\mathrm{.}4022\mathrm{.}2832\mathrm{.}10643\mathrm{.}4653\mathrm{.}1703\mathrm{.}0372\mathrm{.}8552\mathrm{.}58954\mathrm{.}2123\mathrm{.}7913\mathrm{.}6053\mathrm{.}3532\mathrm{.}99164\mathrm{.}9174\mathrm{.}3554\mathrm{.}1113\mathrm{.}7853\mathrm{.}32675\mathrm{.}5824\mathrm{.}8684\mathrm{.}5644\mathrm{.}1603\mathrm{.}60586\mathrm{.}2105\mathrm{.}3354\mathrm{.}9684\mathrm{.}4873\mathrm{.}83796\mathrm{.}8025\mathrm{.}7595\mathrm{.}3284\mathrm{.}7724\mathrm{.}031107\mathrm{.}3606\mathrm{.}1455\mathrm{.}6505\mathrm{.}0194\mathrm{.}192$a$.$Determine the net present value of Project $1$ over a $3-$year life with residual value, assuming a minimum rate of return of $20\%.$ If required, round to the nearest dollar. fill in the blank $1$ of $1$$b$.$Which project provides the greatest net present value?