NA Simple interest vs compound interest (10+)

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Adelle Colbourn

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4 years, 7 months ago

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Adelle Colbourn 4 years, 5 months ago

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Adelle Colbourn 4 years, 7 months ago

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Adelle Colbourn 4 years, 8 months ago

Created this as a copy of NA Simple interest and compound interest.

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Question statement

Simple interest can be calculated using the formula

$\begin{aligned} I &= P \times r \times n \end{aligned}$

Compound interest can be calculated using the formulae

$A = P \times (1+r)^n$ and $I = A - P$

where for all formulae:

$\begin{aligned} \quad I \quad & \text{is the interest earned,} \\ \quad P \quad & \text{is the principal,} \\ \quad r \quad & \text{is the interest rate per time period (as a decimal),} \\ \quad n \quad & \text{is the number of time periods,} \\ \quad A \quad & \text{is the final amount.} \end{aligned}$

Give any introductory information the student needs.

			Name	Type	Generated Value

principal	integer	21000
rate	number	2.5
months	integer	42
simpleinterest	number	1837.5
amount	number	22914.0471286676
compoundinterest	number	1914.0471286676
answer	number	77
names	list	List of 8 items
name1	string	Abraham

Automatically regenerate variables?

Name

Data type

Value

A random number between and (inclusive) with step size

Description

The amount invested.

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

Can an exam override the value of this variable?

Generated value: `integer`

21000

→ Used by:

amount
compoundinterest
simpleinterest

"Unnamed part" - prompt

Advice

Simple interest:

$P = \$ \var{formatnumber(principal,'si-en')}$

$\begin{aligned} r &= \var{rate} ÷ 100 \\ &= \var{rate/100} \end{aligned}$

$\begin{aligned} n &= \var{months} ÷ 12 \\ &= \var{months ÷12} \text{ years} \end{aligned}$

$\begin{aligned} I &= P \times r \times n \\ &= \$ \var{formatnumber(principal,'si-en')} \times \var{rate/100} \times \var{months ÷ 12} \\&= \$ \var{trim(dpformat(simpleinterest,2,'si-en'))} \end{aligned}$

The simple interest is $ {trim(dpformat(simpleinterest,2,'si-en'))} to the nearest cent.

Compound interest was given as ${trim(dpformat({compoundinterest},2,"si-en"))}

How much less:

The question asked how much less interest {name1} would have earnt if simple interest had been calculated.

Compound interest - simple interest

$\begin{aligned} &= \$ \var{trim(dpformat({compoundinterest},2,"si-en"))} - \$ \var {trim(dpformat(simpleinterest,2,'si-en'))} \\ &= \$ \var{trim(dpformat((precround(compoundinterest,2)-precround(simpleinterest,2)),2,'si-en'))} \end{aligned}$

Rounded to the nearest dollar, {name1} would have earnt ${answer} less from the simple interest compared to the compound interest.

Give a worked solution to the whole question.

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This question is used in the following exams:

Timed Practice Quiz v2 by Adelle Colbourn in Odds and Ends.
Timed Practice Quiz v3 by Adelle Colbourn in Odds and Ends.
Lantite (Numeracy) 75 minute practice quiz by Ben Brawn in LANTITE (Numeracy).
Percentages questions repository by Adelle Colbourn in MESH.
Bridging General Maths Quiz 3 by Kate Vincent in Kate's workspace.

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NA Simple interest vs compound interest (10+)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

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Adelle Colbourn 4 years, 5 months ago

Adelle Colbourn 4 years, 7 months ago

Adelle Colbourn 4 years, 8 months ago

Adelle Colbourn 4 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Number entry

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Error

NA Simple interest vs compound interest (10+)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Adelle Colbourn 4 years, 5 months ago

Adelle Colbourn 4 years, 7 months ago

Adelle Colbourn 4 years, 8 months ago

Adelle Colbourn 4 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Number entry

Advanced settings

Generated value: `integer`