# Interest

## Practise calculating simple interest and compound interest on investments and loans.

##### CompareLevel 1Level 2Level 3Level 4Level 5Exam-StyleDescriptionHelpMore Finance

This is level 5; Interest calculated half-yearly, quarterly or monthly. Give all of your answers to two decimal places. You can earn a trophy if you get at least 7 correct and you do this activity online.

 Find the total value of an investment if £350 is invested at 2.2% pa for 10 years compounded twice yearly? £ Find the total value of an investment if £190 is invested at 3.6% pa for 10 years compounded monthly? £ Calculate the interest earned by an investment if $2440 which is invested at 4.5% pa for 10 years compounded quarterly.$ Calculate the interest earned by an investment if $5676 which is invested at 3.9% pa for 9 years compounded every six months.$ If €900 is invested at 1.6% pa for 5 years compounded monthly, find the overall percentage growth of the €900 during the 5 years. % Jennifer has the choice of two savings plans in which she can invest £330 for 7 years. The first plan offers a rate of 1.2% pa compounded monthly. The second plan offers a rate of 1.8% pa compounded twice each year. How much more money will Jennifer make if she chooses the best plan? £ A famous actor invests £1800 in a high interest savings scheme which offered a rate of 3.2% pa compounded twice yearly. After five years the scheme began compounding monthly. How much was the investment worth after 10 years? £ The total value of an investment was $997.45 after$760 was invested for 6 years compounded monthly. Find the interest rate. % Find the number of years it would take for the value of an investment to be worth $898.67 if an original amount of$340.00 was invested at a rate of 5.8% compounded twice yearly. [Give your answer to this question to the nearest whole number of years.] An investment of $$x$$ dollars grows to $$3x$$ dollars after five years in an special super-high interest account compounding anually. Find the interest rate to two decimal places.
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This is Interest level 5. You can also try:
Level 1 Level 2 Level 3 Level 4

## Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

## Transum.org

This web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available.

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#### Connect 4 Factors

A mathematical version of the popular Connect 4 game based on getting four numbers with a common factor in a line. Fun for one, two or a whole class of pupils.

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## Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

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## Teachers

If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

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Scan the QR code below to visit the online version of this activity.

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## Description of Levels

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Percentages - Before starting the Interest exercise make sure you are confident finding percentages of quantities.

Compare: - A table to be filled in Comparing the results of investing with simple interest against the results of investing with compound interest.

Level 1 - Investments earning simple interest

Level 2 - Investments earning compound interest

Level 3 - Loans accruing compound interest

Level 4 - Appreciation and depreciation

Level 5 - Interest calculated half-yearly, quarterly or monthly

Overdraft Charges - Do you understand how your bank charges you for taking out an overdraft?

Amortisation and Annuities - An exercises containing problems about gradually paying off loans and calculating pension plans.

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

More on this topic including lesson Starters, visual aids, investigations and self-marking exercises.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

## Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

## Compound Interest Formulas

$$\text{Final amount} = P(1 + \frac{r}{100k})^{nk}$$
$$\text{Interest earned} = P(1 + \frac{r}{100k})^{nk} - P$$

$$P$$ is the principal, the amount originally invested.

$$r$$ is the rate of interest expressed as a percentage.

$$n$$ is the number of years the amount was invested for.

$$k$$ is the number of compounding periods per year.

If you are following a syllabus that allows the use of a graphic display calculator you could use the Finance Solver to help calculate answers for the compound interest questions.

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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