Exam version Savings compound interest 3

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Julie Crowley

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Julie Crowley 7 years ago

Created this as a copy of Savings compound interest 3.

Name	Status	Author	Last Modified
Savings compound interest 3	Ready to use	Julie Crowley	07/10/2016 22:22
Exam version Savings compound interest 3	draft	Julie Crowley	16/04/2018 17:26
Simon's copy of Savings compound interest 3	draft	Simon Thomas	30/05/2019 10:17
Savings compound interest 3	Ready to use	Xiaodan Leng	27/10/2020 17:06

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Question statement

Two rival high street banks offer customers a new deposit account.

Bank A offers an account that earns interest at a rate of $\var{perc1}$ % per annum where interest is compounded annually.

Bank B offers an account that earns interest at a nominal rate of $\var{perc2}$ % per annum where interest is compounded daily.

Suppose that a potential customer has € $\var{P}$ to invest for $\var{n1}$ years.

The compound interest formula is:

$\ A = P(1+i)^n$

You may assume that there are 365 days per annum.

Give any introductory information the student needs.

			Name	Type	Generated Value

perc1	number	5.9
perc2	number	5.4
int1	number	0.059
int2	number	0.0001479452
n1	integer	3
n2	integer	1095
P	integer	3800
A1	number	4513.06
A2	number	4468.22
int3	number	0.0147945205

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Describe what this variable represents, and list any assumptions made about its value.

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Generated value: `number`

5.9

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Ask the student a question, and give any hints about how they should answer this part.

Suppose that the potential customer chooses Bank A.

What is the value of $n$ ?

Gap 0.

What is the value of $i$ ?

Gap 1.

What is the value of $A$ ? Please give your answer to the nearest cent.

€Gap 2.

Advice

The compound interest formula is: $\ A = P(1+i)^n$

Part (a)

n represents the number of compounding periods , so for Bank A it is $\var{n1}$ years.

i represents the rate of compound interest, for Bank A, the annual interest rate is $\var{perc1}$ % so i is $\frac {\var{perc1}} {100}=\var{int1}$ .

The total amount saved after $\var{n1}$ years is denoted by A. Using the compound interest formula:

$A=P(1+i)^n$

$A=\var{P} \times(1+\var{int1})^\var{n1}=\var{A1}$

Part(b)

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.

the interest rate is ${\var{perc2}}$ % per annum compounded daily.

The interest rate per day is $\frac{\var{perc2}}{365}=\var{int3}$ %

Therefore $i=\frac{\var{int3}}{100}=\var{int2}$

The amount saved after $\var{n1}$ years is denoted by A. Using the compound interest formula:

$A=P(1+i)^n$

$A=\var{P} \times(1+\var{int2})^\var{n2}=\var{A2}$

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Julie Crowley 7 years ago

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Exam version Savings compound interest 3

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Julie Crowley 7 years ago

Error in variable testing condition

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Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`