# Interest

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

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This is level 3; Loans accruing compound interest. Give your first nine answers to two decimal places. You can earn a trophy if you get at least 9 correct and you do this activity online.

 Find the amount of interest accrued if... ...£310 is borrowed at 2% pa compound interest for 6 years. £ ...$540 is borrowed at 1% pa compound interest for 16 years.$ ...€232 is borrowed at 4% pa compound interest for 6 years. € Find the total amount of repayment required if ... ...£410 is borrowed at 1% pa compound interest for 8 years. £ ...$410 is borrowed at 4% pa compound interest for 14 years.$ ...€349 is borrowed at 1% pa compound interest for 17 years. € What percentage is the total interest accrued of the original loan if ... ...£250 is borrowed at 2% pa compound interest for 7 years. % ...$810 is borrowed at 1% pa compound interest for 11 years. % ...€551 is borrowed at 2% pa compound interest for 13 years. % How many years would it take for ... ... you to be £541.22 in debt after £500 is borrowed with 2% pa compound interest. Years: ... you to be$2395.17 in debt after \$2190 is borrowed with 1% pa compound interest. Years: ... you to be €368.23 in debt after €274 is borrowed with 3% pa compound interest. Years:
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This is Interest level 3. You can also try:
Level 1 Level 2 Level 4 Level 5 Level 6 Level 7

## 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.

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An interactive online activity requiring logical thinking and a certain amount of luck. Numbers 1 to 6 are presented randomly and are to be used to produce two 2-digit numbers. Can you ensure that the first number is greater than the second?

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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

Level 6 - Additional payments made during the investment period

Level 7 - Artificial intelligence generated questions

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.

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## Curriculum Reference

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

## Compound Interest Formulas

$$\text{Total repayment} = P(1 + \frac{r}{100})^n$$
$$\text{Interest paid} = P(1 + \frac{r}{100})^n - P$$

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

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

$$n$$ is the number of years the loan was taken out for.

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.

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Transum subscriber Ann never fails to come up with some really interesting observations. Recently she has been time travelling:

“When I first used the compound interest formula it was introduced as the ‘future value’ formula.

Have you ever travelled back in time and used a negative value for n in the formula?

Surprisingly there’s no mention of using the formula when n is negative.  Why do you think that is?

I think it’s a wonderful thing to notice that the compound interest formula can be used without any rearranging to find future values or past values.  I’d be interested to get your opinion.

Maybe it’s just easier for students to think of multiplying by (1+r)n to find the future value and to divide by (1+r)n when finding the past value?”

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