Compare two savings accounts with different interest rates.
\nrebelmaths
"}, "preamble": {"js": "", "css": ""}, "ungrouped_variables": ["perc1", "perc2", "int1", "int2", "n1", "n2", "P", "A1", "A2", "int3"], "variablesTest": {"condition": "", "maxRuns": 100}, "variable_groups": [], "functions": {}, "tags": [], "rulesets": {}, "parts": [{"showCorrectAnswer": true, "variableReplacements": [], "prompt": "Suppose that the potential customer chooses Bank A.
\nWhat is the value of $n$?
\n[[0]]
\nWhat is the value of $i$?
\n[[1]]
\nWhat is the value of $A$? Please give your answer to the nearest cent.
\n€[[2]]
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\nWhat is the value of $n$?
\n[[0]]
\nWhat is the value of $i$? 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 cent.
\n€[[2]]
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\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+i)^n $
\n\nYou may assume that there are 365 days per annum.
\n", "extensions": [], "advice": "
The compound interest formula is: $\\ A = P(1+i)^n $
\nPart (a)
\nn represents the number of compounding periods , so for Bank A it is $\\var{n1}$ years.
\ni represents the rate of compound interest, for Bank A, the annual interest rate is $\\var{perc1}$% so i 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$A=P(1+i)^n$
\n$A=\\var{P} \\times(1+\\var{int1})^\\var{n1}=\\var{A1}$
\nPart(b)
\nn 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.
\ni 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 $i=\\frac{\\var{int3}}{100}=\\var{int2}$
\nThe amount saved after $\\var{n1}$ years is denoted by A. Using the compound interest formula:
\n$A=P(1+i)^n$
\n$A=\\var{P} \\times(1+\\var{int2})^\\var{n2}=\\var{A2}$
", "type": "question", "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}], "resources": []}]}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}]}