// Numbas version: exam_results_page_options {"name": "current value of a share with constant dividend", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"preventleave": false, "allowregen": true, "showfrontpage": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"contributors": [{"profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/", "name": "Ben Brawn"}], "variables": {"Prounded": {"description": "", "name": "Prounded", "definition": "precround(P,2)", "templateType": "anything", "group": "Ungrouped variables"}, "rr": {"description": "", "name": "rr", "definition": "random(4..10)", "templateType": "anything", "group": "Ungrouped variables"}, "D": {"description": "", "name": "D", "definition": "Dcents/100", "templateType": "anything", "group": "Ungrouped variables"}, "Dcents": {"description": "", "name": "Dcents", "definition": "random(5..199)", "templateType": "anything", "group": "Ungrouped variables"}, "P": {"description": "", "name": "P", "definition": "D/rrdec", "templateType": "anything", "group": "Ungrouped variables"}, "rrdec": {"description": "", "name": "rrdec", "definition": "rr/100", "templateType": "anything", "group": "Ungrouped variables"}}, "advice": "

We are asked to find the current value of a share with a constant dividend, therefore we will use the formula

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$\\displaystyle P_0=\\frac{D_0}{r_s}$

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In our situation we have,

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$D_0=\\var{D}$,

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$r_s=\\var{rr}\\%=\\var{rrdec}$,

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and therefore we have

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$\\displaystyle P_0=\\frac{\\var{D}}{\\var{rrdec}}$

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which upon calculation gives

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$\\$\$ [[0]] (to the nearest cent)

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