// Numbas version: exam_results_page_options {"question_groups": [{"name": "Group", "pickQuestions": 1, "pickingStrategy": "all-shuffled", "questions": [{"name": "Numerical reasoning - average salary", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "functions": {"commanumber": {"definition": "var parts=n.toString().split(\".\");\n if(parts[1] && parts[1].length<2) {\n parts[1]+='0';\n }\n return parts[0].replace(/\\B(?=(\\d{3})+(?!\\d))/g, \",\") + (parts[1] ? \".\" + parts[1] : \"\");", "type": "string", "language": "javascript", "parameters": [["n", "number"]]}}, "tags": ["average", "maths-aid", "mean", "money", "numerical reasoning", "percentage", "weighted"], "advice": "

This is a weighted average.

The average value is given by multiplying each salary value by the frequency with which it occurs amongst the staff (in fraction form), and adding the resulting numbers together.

For example, the salary £{commanumber(salary[0])} has a frequency of {per[0]}% which is $\\frac{\\var{per[0]}}{100} = \\var{per[0]/100}$. When we multiply these together we get \\[ £\\var{latex(commanumber(salary[0]))} \\times \\frac{\\var{per[0]}}{100} = \\var{salary[0]*per[0]/100}. \\]

For this question we have 4 salary values and the weighted average is \\[\\begin{align} & \\frac{\\var{per[0]}}{100} \\times \\var{latex(commanumber(salary[0]))} + \\frac{\\var{per[1]}}{100} \\times \\var{latex(commanumber(salary[1]))} + \\frac{\\var{per[2]}}{100} \\times \\var{latex(commanumber(salary[2]))} + \\frac{\\var{per[3]}}{100} \\times \\var{latex(commanumber(salary[3]))} \\\\ &= £\\var{latex(commanumber(salary[0]*per[0]/100))} + £\\var{latex(commanumber(salary[1]*per[1]/100))} + £\\var{latex(commanumber(salary[2]*per[2]/100))} + £\\var{latex(commanumber(salary[3]*per[3]/100))} \\\\ &= £\\var{latex(commanumber(average))} \\end{align} \\]

", "rulesets": {}, "parts": [{"prompt": "

What is the average salary?

£ [[0]]

", "gaps": [{"minvalue": "average", "type": "numberentry", "maxvalue": "average", "marks": 1.0, "showPrecisionHint": false}], "type": "gapfill", "marks": 0.0}], "statement": "

In a department {per[0]}% of the staff have a salary of £{commanumber(salary[0])}, {per[1]}% a salary of £{commanumber(salary[1])}, {per[2]}% a salary of £{commanumber(salary[2])}, and {per[3]}% a salary of £{commanumber(salary[3])}.

", "variable_groups": [], "progress": "ready", "type": "question", "variables": {"salary": {"definition": "shuffle([salary0,salary1,salary2,salary3])", "name": "salary"}, "salary1": {"definition": "random(15000..50000#5000 except salary0)", "name": "salary1"}, "salary0": {"definition": "random(15000..50000#5000)", "name": "salary0"}, "salary3": {"definition": "random(15000..50000#5000 except [salary0,salary1,salary2])", "name": "salary3"}, "salary2": {"definition": "random(15000..50000#5000 except [salary0,salary1])", "name": "salary2"}, "average": {"definition": "(per[0]*salary[0]+per[1]*salary[1]+per[2]*salary[2]+per[3]*salary[3])/100", "name": "average"}, "per": {"definition": "shuffle([per0,per1,per2,per3])", "name": "per"}, "per3": {"definition": "100-per0-per1-per2", "name": "per3"}, "per2": {"definition": "random(10..min(50,90-per0-per1)#10)", "name": "per2"}, "per1": {"definition": "random(10..min(50,80-per0)#10)", "name": "per1"}, "per0": {"definition": "random(10..50#10)", "name": "per0"}}, "metadata": {"notes": "", "description": "

Compute the weighted average salary in a department, given four salary levels and the percentages of staff earning them.

", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Numerical reasoning - lottery syndicate", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["lottery", "maths-aid", "money", "numerical reasoning", "ratio", "shares"], "metadata": {"description": "

Given the stakes of three people in a lottery syndicate, and the amount the syndicate won, work out each person's share of the winnings.

Based on question 4 from section 3.2 of the Maths-Aid workbook on numerical reasoning.

", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

{names[0]}, {names[1]} and {names[2]} agree to buy {numbernames[total]} pounds' worth of lottery tickets, with {names[0]} contributing £{share[0]}, {names[1]} contributing £{share[1]} and {names[2]} contributing £{share[2]}.

They agree that if they win anything with any of these tickets that it should be shared out in the same ratio as their contributions.

", "advice": "

Their agreement means that the winnings should go to {names[0]}, {names[1]} and {names[2]} in the ratio $\\var{share[0]}:\\var{share[1]}:\\var{share[2]}$. Think of these as being shares in the winnings.

There are $\\var{share[0]}+\\var{share[1]}+\\var{share[2]} = \\var{total}$ shares in all for the £{win}.

Hence each share is worth $£\\var{win} \\div \\var{total} = £\\var{part}$.

So {names[0]} gets {share[0]} {pluralise(share[0],'share','shares')} = $\\var{share[0]} \\times £\\var{part} = £\\var{winnings[0]}$, {names[1]} {share[1]} {pluralise(share[1],'share','shares')} = $\\var{share[1]} \\times £\\var{part} = £\\var{winnings[1]}$ and {names[2]} {share[2]} {pluralise(share[2],'share','shares')} = $\\var{share[2]} \\times £\\var{part} = £\\var{winnings[2]}$.

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"numbernames": {"name": "numbernames", "group": "Ungrouped variables", "definition": "['zero','one','two','three','four','five','six','seven','eight','nine','ten','eleven','twelve','thirteen','fourteen','fifteen','sixteen','seventeen','eighteen','nineteen']", "description": "", "templateType": "anything", "can_override": false}, "winnings": {"name": "winnings", "group": "Ungrouped variables", "definition": "map(x*part,x,share)", "description": "", "templateType": "anything", "can_override": false}, "names": {"name": "names", "group": "Ungrouped variables", "definition": "shuffle(['Bob','Terry','Cilla','Jim','Margaret','Cyril','Ethel','Horace','Beryl'])[0..3]", "description": "", "templateType": "anything", "can_override": false}, "share": {"name": "share", "group": "Ungrouped variables", "definition": "shuffle([share0,share1,share2])", "description": "", "templateType": "anything", "can_override": false}, "share1": {"name": "share1", "group": "Ungrouped variables", "definition": "random(1..min(floor(total/2),total-1-share0))", "description": "", "templateType": "anything", "can_override": false}, "share0": {"name": "share0", "group": "Ungrouped variables", "definition": "random(1..floor(total/2))", "description": "", "templateType": "anything", "can_override": false}, "share2": {"name": "share2", "group": "Ungrouped variables", "definition": "total-share0-share1", "description": "", "templateType": "anything", "can_override": false}, "part": {"name": "part", "group": "Ungrouped variables", "definition": "win/total", "description": "", "templateType": "anything", "can_override": false}, "win": {"name": "win", "group": "Ungrouped variables", "definition": "random(2..10)*total*5", "description": "", "templateType": "anything", "can_override": false}, "total": {"name": "total", "group": "Ungrouped variables", "definition": "random(6..15)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["numbernames", "winnings", "names", "share", "share0", "share1", "share2", "part", "win", "total"], "variable_groups": [], "functions": {"pluralise": {"parameters": [["n", "number"], ["single", "string"], ["plural", "string"]], "type": "string", "language": "javascript", "definition": "return Numbas.util.pluralise(n,single,plural);"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

They win £{win}. How much does each get?

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

{names[0]}	£ [[0]]
{names[1]}	£ [[1]]
{names[2]}	£ [[2]]

", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "winnings[0]", "maxValue": "winnings[0]", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "winnings[1]", "maxValue": "winnings[1]", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "winnings[2]", "maxValue": "winnings[2]", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Numerical reasoning - price markup", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "functions": {}, "tags": ["maths-aid", "money", "numerical reasoning", "percentage", "price", "profit"], "advice": "

In order to realise a profit of {profit}%, the selling price of the item must be {100+profit}% of the cost of production.

This price is $\\frac{\\var{100+profit}}{100} \\times \\var{produce} = £\\var{sell}.$

When rounding this to the nearest penny, a decision has to be made whether the price is £{floor(sell*100)/100} or £{ceil(sell*100)/100}. Usually, if the next digit after the one being rounded is {if(fract(sell*100)<0.5,'less than 5 then we round down','greater than or equal to 5 then we round up')}, so we take the price to be £{dpformat(sell,2)}.

", "rulesets": {}, "parts": [{"prompt": "

Give your answer to the nearest penny.

£ [[0]]

", "gaps": [{"precisiontype": "dp", "precisionmessage": "

You didn't give your answer to the nearest penny. Round your answer to two decimal places.

", "maxvalue": "precround(sell,2)+0.005", "minvalue": "precround(sell,2)-0.005", "precisionpartialcredit": 50.0, "precision": 2.0, "marks": 1.0, "type": "numberentry", "showPrecisionHint": false}], "type": "gapfill", "marks": 0.0}], "statement": "

An item costs £{dpformat(produce,2)} to produce. How much should the manufacturer sell these items for if it wants to realise a profit of {profit}% on these items?

", "variable_groups": [], "progress": "ready", "type": "question", "variables": {"profit": {"definition": "random(5..35#10)", "name": "profit"}, "sell": {"definition": "produce*(1+profit/100)", "name": "sell"}, "produce": {"definition": "random(2..10)+random(0.25,0.75,0.50)", "name": "produce"}}, "metadata": {"notes": "", "description": "

Given the cost to produce an item and a desired markup, calculate the appropriate sale price.

", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Numerical reasoning - tax", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["income", "money", "numerical reasoning", "percentage", "Percentage", "tax"], "metadata": {"description": "

Given an annual salary, tax allowance, tax rate and pension deduction, work out a person's take-home pay per month.

", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

{names} has a salary of £{commanumber(salary)} per year.

{capitalise(he)} has a tax allowance of £{commanumber(allowance)} and {he} pays income tax at {tax}% on the rest.

{capitalise(he)} pays into a pension and for this {his} salary is deducted {pension}% after tax has been deducted.

", "advice": "

{names} is only taxed on the amount remaining after taking away the allowance, i.e. $£\\var{commanumber(salary)} - £\\var{commanumber(allowance)} = £\\var{commanumber(salary-allowance)}.$

Income tax is {tax}% on this $£\\var{commanumber(salary-allowance)}$ and is $£\\var{latex(commanumber(salary-allowance))} \\times \\frac{\\var{tax}}{100} = £\\var{commanumber(taxedincome)}.$

This leaves {names} with $£\\var{commanumber(salary)} - £\\var{commanumber(taxedincome)} = £\\var{commanumber(aftertax)}.$

{pension}% of this is for {his} pension contributions, i.e. $£\\var{commanumber(aftertax)} \\times \\frac{\\var{pension}}{100} = £\\var{commanumber(pensiondeduction)}.$

The amount left is then $£\\var{commanumber(aftertax)} - £\\var{commanumber(pensiondeduction)} = £\\var{commanumber(precround(netincome,2))}.$

The take home pay per month is hence $\\frac{\\var{netincome}}{12} = £\\var{commanumber(incomepermonth)}$, to the nearest penny.

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"salary": {"name": "salary", "group": "Ungrouped variables", "definition": "random(18000..50000#1000)", "description": "", "templateType": "anything", "can_override": false}, "aftertax": {"name": "aftertax", "group": "Ungrouped variables", "definition": "salary-taxedincome", "description": "", "templateType": "anything", "can_override": false}, "incomepermonth": {"name": "incomepermonth", "group": "Ungrouped variables", "definition": "precround(netincome/12,2)", "description": "", "templateType": "anything", "can_override": false}, "his": {"name": "his", "group": "Ungrouped variables", "definition": "if(he='he','his','her')", "description": "", "templateType": "anything", "can_override": false}, "names": {"name": "names", "group": "Ungrouped variables", "definition": "if(he='he',random(['Bob','Bill','Ben','Barry']),random(['Bridget','Beth','Bea','Beatrice']))", "description": "", "templateType": "anything", "can_override": false}, "netincome": {"name": "netincome", "group": "Ungrouped variables", "definition": "(allowance+(salary-allowance)*(1-tax/100))*(1-pension/100)", "description": "", "templateType": "anything", "can_override": false}, "pensiondeduction": {"name": "pensiondeduction", "group": "Ungrouped variables", "definition": "aftertax*pension/100", "description": "", "templateType": "anything", "can_override": false}, "tax": {"name": "tax", "group": "Ungrouped variables", "definition": "random(15..30)", "description": "", "templateType": "anything", "can_override": false}, "pension": {"name": "pension", "group": "Ungrouped variables", "definition": "random(3..15)", "description": "", "templateType": "anything", "can_override": false}, "taxedincome": {"name": "taxedincome", "group": "Ungrouped variables", "definition": "(salary-allowance)*tax/100", "description": "", "templateType": "anything", "can_override": false}, "allowance": {"name": "allowance", "group": "Ungrouped variables", "definition": "random(1000..10000#1000)", "description": "", "templateType": "anything", "can_override": false}, "he": {"name": "he", "group": "Ungrouped variables", "definition": "random('he','she')", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["salary", "aftertax", "incomepermonth", "his", "names", "netincome", "pensiondeduction", "tax", "pension", "taxedincome", "he", "allowance"], "variable_groups": [], "functions": {"commanumber": {"parameters": [["n", "number"]], "type": "string", "language": "javascript", "definition": "var parts=n.toString().split(\".\");\n if(parts[1] && parts[1].length<2) {\n parts[1]+='0';\n }\n return parts[0].replace(/\\B(?=(\\d{3})+(?!\\d))/g, \",\") + (parts[1] ? \".\" + parts[1] : \"\");"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

How much does {he} get per month, assuming that these are the only deductions?

£ [[0]] (to the nearest penny)

The amount of money a person gets on their birthday follows an arithmetic sequence.

Calculate the amount on a given birthday, then calculate the sum up to that point.

", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "advice": "

We are told that {person['name']}'s parents deposit a uniformly increasing amount of money into a savings account for {person['name']} every year on {person['name']}'s birthday.

We are also given the amount of money that {person['pronouns']['their']} parents deposit into the account on {person['pronouns']['their']} first $3$ birthdays:

On {person['pronouns']['their']} $1^{st}$ birthday, they deposited $£\\var{first}$ into the account.
On {person['pronouns']['their']} $2^{nd}$ birthday, they deposited $£\\var{b[1]+first}$ into the account.
On {person['pronouns']['their']} $3^{rd}$ birthday, they deposited $£\\var{b[1]*2+first}$ into the account.

a)

To calculate the amount of money {person['name']}'s parents would deposit into the savings account on {person['pronouns']['their']} 21^st birthday, if {pronouns['their']} parents maintained this pattern, we use the equation

\\[a_n=a_1+(n-1)d\\text{,}\\]

where

$a_1$ is the first term;
$a_n$ is the $n^{\\text{th}}$ term;
$d$ is the common difference between consecutive terms.

To identify the first term and common difference of the sequence we can use a table like the one below.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

$n$	$1$	$2$	$3$
$a_n$	$\\mathbf{\\var{first}}$	$\\var{b[1]+first}$	$\\var{b[1]*2+first}$
First differences		$\\mathbf{\\var{b[1]}}$	$\\mathbf{\\var{b[1]}}$

The first term and common difference have been highlighted in bold: $a_1 = \\var{first}$ and $d = \\var{b[1]}$.

Now we can use these to calculate $a_{21}$, giving us

\\begin{align}
a_{21}&=\\var{first}+\\var{b[1]} \\times (21-1) \\\\
&=\\var{first+b[1]*(20)}\\text{.} \\\\
\\end{align}

So, assuming that {person['name']}'s parents do maintain this pattern, on {pronouns['their']} 21^st birthday {pronouns['their']} parents will deposit $£\\var{first+b[1]*(20)}$ into the savings account.

b)

We are now asked to calculate the total amount of money that {person['name']}'s parents will have added to this savings account over 21 years, including the money that {pronouns['their']} parents will deposit into the account on {pronouns['their']} 21^st birthday.

This question involves calculating the sum using the equation

\\[\\sum\\limits_{i=1}^n{a_i}=\\frac{n}{2}(a_1+a_n)\\text{.}\\]

We know from part a) that

\\begin{align}
a_1&=\\var{first},\\\\
n&=21,\\\\
a_{21}&= \\var{first+b[1]*(20)}.
\\end{align}

Using our formula for the sum,

\\begin{align}
\\sum\\limits_{i=1}^n{a_i}&=\\frac{n}{2}(a_1+a_n)\\\\
&=\\frac{\\var{21}}{2}(\\var{first}+\\var{first+b[1]*(21-1)})\\\\
&=\\var{21*(first+first+b[1]*(20))/2}\\text{.}
\\end{align}

Therefore, over 21 years {person['name']}'s parents will have added a total of $£\\var{21*(first+first+b[1]*(20))/2}$ to this savings account!

", "statement": "

{person['name']}'s parents deposit a uniformly increasing amount of money into a savings account for {pronouns['them']} every year on {pronouns['their']} birthday:

on {pronouns['their']} first birthday {pronouns['their']} parents deposited $£\\var{first}$ into the account;
on {pronouns['their']} second birthday {person['pronouns']['their']} parents deposited $£\\var{b[1]+first}$ into the account;
on {pronouns['their']} third birthday {pronouns['their']} parents deposited $£\\var{b[1]*2+first}$ into the account.

{person['name']} wants to know the total amount of money that will be in this savings account, excluding interest, after {pronouns['their']} 21^st birthday, if {pronouns['their']} parents maintain this pattern.

", "preamble": {"js": "", "css": ""}, "variables": {"c": {"name": "c", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "repeat(random(3..13 except[10]),8)"}, "n": {"name": "n", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "repeat(random(3..9),7)"}, "person": {"name": "person", "description": "

A random person

", "templateType": "anything", "group": "A person", "definition": "random_person()"}, "m": {"name": "m", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "repeat(random(2..10),5)"}, "first": {"name": "first", "description": "

first term in the sequence

", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(10..15 #5)"}, "pronouns": {"name": "pronouns", "description": "", "templateType": "anything", "group": "A person", "definition": "person['pronouns']"}, "ni": {"name": "ni", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "repeat(random(19..40),10)"}, "b": {"name": "b", "description": "

", "templateType": "anything", "group": "Ungrouped variables", "definition": "repeat(random(10..25 #5), 3)"}, "ci": {"name": "ci", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "repeat(random(6..20),10)"}}, "parts": [{"variableReplacementStrategy": "originalfirst", "prompt": "

How much money will {person['name']}'s parents deposit into the savings account on {pronouns['their']} 21^st birthday, if {pronouns['their']} parents maintain this pattern?

£[[0]].

", "stepsPenalty": 0, "gaps": [{"answer": "{first+b[1]*(20)}", "showpreview": true, "expectedvariablenames": [], "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "checkingtype": "absdiff", "type": "jme", "checkingaccuracy": 0.001, "variableReplacements": [], "vsetrange": [0, 1], "checkvariablenames": false, "showFeedbackIcon": true, "scripts": {}, "marks": 1, "showCorrectAnswer": true}], "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "type": "gapfill", "marks": 0, "steps": [{"variableReplacementStrategy": "originalfirst", "prompt": "

Use the arithmetic formula,

\\[a_n = a_1 + (n-1)d, \\]

where

$a_n$ is the $n^\\text{th}$ term;
$a_1$ is the first term in the sequence;
$d$ is the common difference between consecutive terms.

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What is the value of $a_1$?

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What is the value of $d$?

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Now use the formula to calculate $a_{21}$.

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How much money will {person['name']}'s parents have added to this savings account over $21$ years in total, including the money that {person['pronouns']['their']} parents will deposit into the account on {person['pronouns']['their']} $21^{st}$ birthday?

£[[0]].

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The sum of an arithmetic sequence $a_1, a_2, \\ldots, a_n$ is calculated by the following formula.

\\[\\sum\\limits_{i=1}^n{a_i}=\\frac{n}{2}(a_1+a_n)\\text{.}\\]

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Suppose a loan of £{value} is to be repaid by the amount of £{value1} at the end of two months. What is the annual rate of simple interest,i in %?

[[0]]%

How long does it take for £{value} to earn £{value2} at {int}% p.a simple interest? Answer in %

[[0]]%

The yield on a deposit is {int1}% on the ACT/360 basis. What is the equivalent yield on an ACT/365 basis? Answer in %

[[0]]%

£{value3} is deposited with a bank on 10 May 2014 and withdrawn at the same time of the day on 20 september 2014. Find the accumulated value if the interest rate is {int2}% simple interest.

£[[0]]

How long will it take for £{value4} to accumulate to £{value5} at {int3}% p.a? [[0]] Years

A necklace is appraised at £{value6}. If the value of the necklace has increased at an annual rate of {int4}%, how much was it worth {years} years ago?

£ [[0]]

Suppose, force of interest, δ = {int5}%. What is the effective annual rate of interest? Answer in %.

[[0]]%

If a fund of £1 accumulates at a force of δ(t)=0.02t, find the accumulated amount over 2 years as well as the annual effective rate of interest.

Accumulated amount:[[0]]

interest rate in %:[[1]]%

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$1+i=(1+\\frac{i^{(p)}}{p})^p$

$1+i=e^{\\delta }$

$v_{i}=\\frac{1}{1+i}=e^{-\\delta }$

$d=1-v_{i}$

$A(n)=1+in$

$A(n)={(1+i)}^n$

$A(n)=(1+\\frac{i^{(p)}}{p})^{pn}$

$A(n)=e^{{\\delta}n}$

$A(n)=e^{\\int_{0}^{n}\\delta (t) dt)}$

$1+i_M=(1+i_R)(1+q)$

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Questions about percentage and ratio, applied to finance.

Based on section 3.2 of the Maths-Aid workbook on numerical reasoning.

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