# Interest

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

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This is level 4; Appreciation and depreciation. 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.

 A house is bought for £286,000. In each of the six years that follow, its value appreciates by 6%. How much is the house worth after the six years? £ I buy a new phone for £331. It depreciates in value by 9.4% per year. How much is the phone worth eight years later? £ Paddy buys a vintage car for $20700. Its value appreciates by 4% each year. After three years how much is it worth?$ I buy a laptop for $966. It falls in value by 6.3% anually. How much is the laptop worth after seven years?$ When Atua received a bitcoin for his 18th birthday it was worth £7886. In each of the four years that followed, its value increased by 4.33%. How much was one bitcoin worth after the four years? £ The value of a large screen TV decreases by a fixed percentage of its value at the beginning of the year. A new TV was worth £1332 when purchased but had decreased in value to £1225.44 by the end of the first year. How much was the TV worth after seven years? £ Brayden buys a painting for $600,000. Its value appreciates by 6.9% each year. He decides to sell the painting at the end of the year its value first exceeds one million dollars; How much profit will Brayden make?$ An antique jar cost £551 and its value increased by 7.3% anually. After how many years did it first exceed twice its original value? [Give your answer to this question as whole number of years.] An antique box cost £1357 and its value increased by 7.3% anually. After how many years did it first exceed twice its original value? [Give your answer to this question as whole number of years.] An ancient Roman coin cost £450 and its value increased by 5.3% each year. In which year did the value of the coin first appreciate by more than £100? [Give your answer to this question as whole number of years.]
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This is Interest level 4. You can also try:
Level 1 Level 2 Level 3 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.

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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 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.

## Definitions

Appreciation is an increase in the value of an asset over time.

Depreciation is the decrease in the value of an asset over time.

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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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