On April $12,2021,$ Prism Ltd$.,$ a camera lens manufacturer, purchased real estate for $$552,775.$ Prism paid cash of $$75,000$ and incurred a mortgage payable for the balance. The company also paid $$29,400$ cash in closing costs. The real estate included land appraised at $$249,577$; land improvements appraised at $$83,240$; and a building appraised at $$261,360.$ Prepare a calculation showing the allocation of the total cost among the three purchased assets and present the journal entry to record the purchase.