At the end of $2020,$ Mr$.$ Vaughn sold both his city home and his summer cottage$.$ Every year he has spent at least a portion of the year living in each of the two locations. When he is not residing in these properties they are left vacant. Relevant information on the two properties is as follows: City Home Cottage Year acquired $20032003$ Cost $$264,000$ $ $36,000$ Gross proceeds from sale $528,000330,000$ Real estate commissions $32,00016,000$ Mr$.$ Vaughn wishes to minimize any capital gains resulting from the sale of the two properties. Required: Describe how the residences should be designated in order to accomplish Mr$.$ Vaughns goal. In addition, calculate the amount of the gain that would arise under the designation that you have recommended? Principle residence formula: $((1+$number of years designated$)/$number of years owned$)$X gain