Suppose that the potential customer chooses Bank A.
\nWhat is the value of $n$?
\n[[0]]
\nWhat is the value of $r$?
\n[[1]]
\nWhat is the value of $A$? Please give your answer to the nearest penny.
\n£[[2]]
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\nWhat is the value of $n$?
\n[[0]]
\nWhat is the value of $r$? Please include all the decimal places in your answer.
\n[[1]]
\n\nWhat is the value of $A$? Please give your answer to the nearest penny.
\n£[[2]]
\n", "variableReplacementStrategy": "originalfirst", "unitTests": [], "useCustomName": false, "marks": 0, "type": "gapfill"}], "functions": {}, "name": "Simon's copy of Savings compound interest 3", "tags": [], "extensions": [], "variablesTest": {"condition": "", "maxRuns": 100}, "variable_groups": [], "ungrouped_variables": ["perc1", "perc2", "int1", "int2", "n1", "n2", "P", "A1", "A2", "int3"], "variables": {"n2": {"definition": "n1*365", "group": "Ungrouped variables", "description": "", "name": "n2", "templateType": "anything"}, "int1": {"definition": "perc1/100", "group": "Ungrouped variables", "description": "", "name": "int1", "templateType": "anything"}, "perc2": {"definition": "random(5.0..5.8#0.1)", "group": "Ungrouped variables", "description": "", "name": "perc2", "templateType": "anything"}, "A2": {"definition": "precround(P*(1+int2)^n2,2)", "group": "Ungrouped variables", "description": "", "name": "A2", "templateType": "anything"}, "P": {"definition": "random(2000..5000#100)", "group": "Ungrouped variables", "description": "", "name": "P", "templateType": "anything"}, "n1": {"definition": "random(2..4#1)", "group": "Ungrouped variables", "description": "", "name": "n1", "templateType": "anything"}, "A1": {"definition": "precround(P*(1+int1)^n1,2)", "group": "Ungrouped variables", "description": "", "name": "A1", "templateType": "anything"}, "int2": {"definition": "perc2/36500", "group": "Ungrouped variables", "description": "", "name": "int2", "templateType": "anything"}, "int3": {"definition": "perc2/365", "group": "Ungrouped variables", "description": "", "name": "int3", "templateType": "anything"}, "perc1": {"definition": "random(5.2..6#0.1)", "group": "Ungrouped variables", "description": "", "name": "perc1", "templateType": "anything"}}, "rulesets": {}, "preamble": {"css": "", "js": ""}, "advice": "The compound interest formula is: $\\ A = P(1+r)^n $
\n\n
(a)
\n$n$ represents the number of compounding periods , so for Bank A it is $\\var{n1}$ years.
\n$r$ represents the rate of compound interest, for Bank A, the annual interest rate is $\\var{perc1}$% so $r$ is $\\frac {\\var{perc1}} {100}=\\var{int1}$.
\nThe total amount saved after $\\var{n1}$ years is denoted by $A$. Using the compound interest formula:
\n$A=P(1+r)^n$
\n$A=\\var{P} \\times(1+\\var{int1})^\\var{n1}=£\\var{dpformat(A1,2)}$
\n\n
(b)
\n$n$ represents the number of compounding periods. For Bank B, interest is compounded daily for $\\var{n1}$ years so there are a total of $365 \\times \\var{n1} =\\var{n2}$ compounding periods.
\n$r$ represents the rate of compound interest. For Bank B, the interest rate is ${\\var{perc2}}$% per annum compounded daily.
\nThe interest rate per day is $\\frac{\\var{perc2}}{365}=\\var{int3}$%
\nTherefore $r=\\frac{\\var{int3}}{100}=\\var{int2}$
\nThe amount saved after $\\var{n1}$ years is denoted by $A$. Using the compound interest formula:
\n$A=P(1+r)^n$
\n$A=\\var{P} \\times(1+\\var{int2})^\\var{n2}=£\\var{dpformat(A2,2)}$
", "metadata": {"description": "Compare two savings accounts with different interest rates.
\nrebelmaths
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "Two rival high street banks offer customers a new deposit account.
\nBank A offers an account that earns interest at a rate of $\\var{perc1}$% per annum where interest is compounded annually.
\nBank B offers an account that earns interest at a nominal rate of $\\var{perc2}$% per annum where interest is compounded daily.
\nSuppose that a potential customer has £$\\var{P}$ to invest for $\\var{n1}$ years.
\nThe compound interest formula is:
\n$\\ A = P(1+r)^n $
\n\nYou may assume that there are 365 days per annum.
\n", "type": "question", "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}]}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}