# Interest

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

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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 £100 is invested at 5.6% pa for 10 years compounded twice yearly? £ Find the total value of an investment if £510 is invested at 5.9% pa for 5 years compounded monthly? £ Calculate the interest earned by an investment if $7570 which is invested at 1.5% pa for 9 years compounded quarterly.$ Calculate the interest earned by an investment if $4647 which is invested at 5.5% pa for 8 years compounded every six months.$ If €510 is invested at 3.5% pa for 8 years compounded monthly, find the overall percentage growth of the €510 during the 8 years. % Noah has the choice of two savings plans in which he can invest £350 for 6 years. The first plan offers a rate of 3.1% pa compounded monthly. The second plan offers a rate of 3.8% pa compounded twice each year. How much more money will Noah make if he chooses the best plan? £ A famous actor invests £8600 in a high interest savings scheme which offered a rate of 5.1% 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 $298.09 after$230 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 $1222.54 if an original amount of$890.00 was invested at a rate of 3.2% 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 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.

## 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.

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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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