// Numbas version: exam_results_page_options {"name": "Simon's copy of Net Present Value 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variables": {"PV1": {"templateType": "anything", "name": "PV1", "definition": "precround(Return1/(1+int)^n1,2)", "description": "", "group": "Ungrouped variables"}, "num": {"templateType": "anything", "name": "num", "definition": "(1+int)^n1", "description": "", "group": "Ungrouped variables"}, "num2": {"templateType": "anything", "name": "num2", "definition": "(1+int)^n2", "description": "", "group": "Ungrouped variables"}, "Return1": {"templateType": "anything", "name": "Return1", "definition": "random(20000..30000#5000)", "description": "", "group": "Ungrouped variables"}, "int": {"templateType": "anything", "name": "int", "definition": "perc/100", "description": "", "group": "Ungrouped variables"}, "n2": {"templateType": "anything", "name": "n2", "definition": "n1+3", "description": "", "group": "Ungrouped variables"}, "n1": {"templateType": "anything", "name": "n1", "definition": "random(2..4#1)", "description": "", "group": "Ungrouped variables"}, "perc": {"templateType": "anything", "name": "perc", "definition": "random(2..6#0.5)", "description": "", "group": "Ungrouped variables"}, "PV2": {"templateType": "anything", "name": "PV2", "definition": "precround(Return2/(1+int)^n2,2)", "description": "", "group": "Ungrouped variables"}, "NPV": {"templateType": "anything", "name": "NPV", "definition": "(PV1+PV2)- INVEST", "description": "", "group": "Ungrouped variables"}, "Invest": {"templateType": "anything", "name": "Invest", "definition": "siground(Return1/(1+int+0.01)^n1+Return2/(1+int+0.01)^n2, 3)", "description": "", "group": "Ungrouped variables"}, "Return2": {"templateType": "anything", "name": "Return2", "definition": "random(40000..70000#5000)", "description": "", "group": "Ungrouped variables"}}, "tags": [], "parts": [{"sortAnswers": false, "variableReplacements": [], "gaps": [{"variableReplacements": [], "minValue": "NPV-0.01", "precisionPartialCredit": 0, "allowFractions": false, "mustBeReducedPC": 0, "precisionMessage": "You have not given your answer to the correct precision.", "customMarkingAlgorithm": "", "showPrecisionHint": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain", "type": "numberentry", "maxValue": "NPV+0.01", "marks": "3", "scripts": {}, "strictPrecision": false, "mustBeReduced": false, "extendBaseMarkingAlgorithm": true, "customName": "", "showCorrectAnswer": true, "correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "unitTests": [], "variableReplacementStrategy": "originalfirst", "precision": "2", "precisionType": "dp", "useCustomName": false}], "extendBaseMarkingAlgorithm": true, "customName": "", "prompt": "

Calculate the net present value (NPV) of the investment given that the discount rate is $\\var{perc}$% per annum. Give your answer to the nearest penny.

£[[0]]

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We wish to calculate the net present value (NPV) of an investment that will be worth £$\\var{Return1}$ in $\\var{n1}$ years time plus an additional £$\\var{Return2}$ in $\\var{n2}$ years time. Using the present value formula, the present value of the £$\\var{Return1}$ is:

$P=\\frac{A}{(1+r)^{n}}$

where $A$ is £$\\var{Return1}$, $n$ is $\\var{n1}$ and $r$ is $\\frac{\\var{perc}}{100}=\\var{int}$

$P1=\\frac{\\var{Return1}}{(1+\\var{int})^{\\var{n}}}$

$P1=\\frac{\\var{Return1}}{\\var{num}}$

$P1=\\var{PV1}$

Using the present value formula, the present value of the £$\\var{Return2}$ is:

$P=\\frac{A}{(1+r)^{n}}$

where $A$ is £$\\var{Return2}$, $n$ is $\\var{n2}$ and $r$ is $\\frac{\\var{perc}}{100}=\\var{int}$

$P2=\\frac{\\var{Return2}}{(1+\\var{int})^{\\var{n}}}$

$P2=\\frac{\\var{Return2}}{\\var{num}}$

$P2=\\var{PV2}$

The NPV of the total amount is $P1+P2-$Investment$=\\var{PV1}+\\var{PV2}-\\var{INVEST}=£\\var{NPV}$

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An investment of £$\\var{Invest}$ invested today will give a return of £$\\var{Return1}$ in $\\var{n1}$ years' time and a further return of £$\\var{Return2}$ in $\\var{n2}$ years' time.

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An investment of x invested today will give a return of €y in n1 years time and a further €z n2 years from today. Calculate the net present value (NPV) of the investment given that the discount rate is perc% per annum.

rebelmaths

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