# Interest

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

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This is level 7; Artificial intelligence generated questions. 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.

The following ten questions were generated by a computer using artificial intelligence (a generative pre-trained transformer). The software reacted to the input "Create a set of 10 interesting questions to practice working out compound interest ordered from easiest to hardest". I don't think the questions are particularly interesting but they do show progression in the sophistication of the calculation required.

 If you deposit $100 into a savings account that earns 2% interest per year, how much will you have after 1 year?$ If you deposit $1,000 into a savings account that earns 5% interest per year, how much will you have after 3 years?$ If you deposit $5,000 into a savings account that earns 3% interest per year, how much will you have after 5 years if the interest is compounded annually?$ If you deposit $10,000 into a savings account that earns 4% interest per year, how much will you have after 10 years if the interest is compounded quarterly?$ If you borrow $50,000 at an annual interest rate of 6%, how much will you need to pay back after 5 years if the interest is compounded monthly?$ If you borrow $100,000 at an annual interest rate of 7%, how much will you need to pay back after 10 years if the interest is compounded daily?$ If you deposit $5,000 into a savings account that earns 3% interest per year, how much will you have after 10 years if the interest is compounded continuously?$ If you borrow $50,000 at an annual interest rate of 8%, how much will you need to pay back after 7 years if the interest is compounded annually and there is a$500 origination fee? $If you deposit$10,000 into a savings account that earns 5% interest per year, how much will you have after 5 years if the interest is compounded semi-annually and you make monthly deposits of $500?$ If you borrow $100,000 at an annual interest rate of 10%, how much will you need to pay back after 15 years if the interest is compounded quarterly and you make monthly payments of$1,000 towards the principal? \$
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This is Interest level 7. You can also try:
Level 1 Level 2 Level 3 Level 4 Level 5 Level 6

## 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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## 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.

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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