Interest & Depreciation | Edexcel GCSE Maths: Foundation Revision Notes 2017

Simple Interest

What is simple interest?

Interest is money that is regularly added to an original amount of money
- This could be added yearly, monthly, etc
- When saving money, interest helps increase the amount saved
- With debt, interest increases the amount owed
Simple interest refers to interest which is based only on the starting amount
- Each interest payment (or charge in the case of debt) will be the same
To find the total simple interest earned
- Find a percentage (the percentage rate) of the starting amount
  - Use a multiplier to do this (e.g. 0.05 to find 5%)
- Multiply this by the number of time periods (e.g. years) it is being applied for
To find the total amount (or balance) after the simple interest has been earned
- Use the same method as above, and add this on to the starting amount

Examiner Tip

Double check:
- Does the question ask for the interest earned, or the total amount at the end?
- Do you need to round your answer? (e.g. to the nearest hundred)

Worked example

A bank account offers simple interest of 4% per year. Nigel puts £ 250 into this bank account, and leaves it to earn interest for 6 years.

(a)

Find the total amount of interest earned over the 6 year period.

Each year, 4% of the starting amount is added as interest
Find 4% of £ 250 using a multiplier

0.04 × 250 = 10

This amount of interest is earned every year, for 6 years

10 × 6 = 60

£ 60 of interest is earned

(b)

Find the total amount in the bank account at the end of the 6 year period.

Add the amount of interest earned, found in part (a), to the starting amount

250 + 60 = 310

£ 310

Worked example

Noah invests £ 9000 at a rate of $n %$ simple interest per year, for 5 years. At the end of 5 years there is £ 11 700 in the account. Find the value of $n$ .

Find the total amount of interest earned over the 5 years

11 700 - 9 000 = £ 2 700 total interest

As we are dealing with simple interest, the same amount of interest is earned each year
Find the interest earned each year

2 700 ÷ 5 = £ 540 interest per year

Find what percentage of the original amount this represents

$\frac{540}{9000} = 0.06 = 6 %$

£ 540 is 6% of the original £ 9000

$n = 6$

Compound Interest

What is compound interest?

Compound interest is where interest is calculated on the running total, not just the starting amount
- This is different from simple interest where interest is only based on the starting amount
E.g., $ 100 earns 10% interest each year, for 3 years
- At the end of year 1, 10% of $ 100 is earned
  - The total balance will now be 100+10 = $ 110
- At the end of year 2, 10% of $ 110 is earned
  - The balance will now be 110+11 = $ 121
- At the end of year 3, 10% of $ 121 is earned
  - The balance will now be 121+12.1 = $ 133.10

How do I calculate compound interest?

Compound interest increases an amount by a percentage, and then increases the new amount by the same percentage
- This process repeats each time period (yearly or monthly etc)
We can use a multiplier to carry out the percentage increase multiple times
- To increase $ 300 by 5% once, we would find 300×1.05
- To increase $ 300 by 5%, each year for 2 years, we would find (300×1.05)×1.05
  - This could be rewritten as 300×1.05²
- To increase $ 300 by 5%, each year for 3 years, we would find ((300×1.05)×1.05)×1.05
  - This could be rewritten as 300×1.05³
This can be extended to any number of periods that the interest is applied for
- If $ 2000 is subject to 4% compound interest each year for 12 years
- We would find 2000×1.04¹², which is $ 3202.06
Note that this method calculates the total balance at the end of the period, not the interest earned
A similar method can be used if something decreases in value by a percentage every year (e.g. a car)
- This is known as depreciation
- Change the multiplier to one which represents a percentage decrease
  - e.g. a decrease of 15% would be a multiplier of 0.85
- If a car worth $ 16 000 depreciates by 15% each year for 6 years
  - Its value will be 16 000 × 0.85⁶, which is $ 6034.39

Examiner Tip

Double check if the question uses simple interest or compound interest.

Worked example

Jasmina invests $ 1200 in a savings account which pays compound interest at the rate of 4% per year for 7 years.

To the nearest dollar, what is her investment worth at the end of the 7 years?

We want an increase of 4% per year, this is equivalent to a multiplier of 1.04, or 104% of the original amount

This multiplier is applied 7 times; $\times 1.04 \times 1.04 \times 1.04 \times 1.04 \times 1.04 \times 1.04 \times 1.04 = 1 . 04^{7}$

Therefore the final value after 7 years will be

$1200 \times 1 . 04^{7} = $ 1579.118135$

Round to the nearest dollar

$$ 1579$

Interest & Depreciation (Edexcel GCSE Maths: Foundation)

Revision Note

Simple Interest

What is simple interest?

Examiner Tip

Worked example

Worked example

Compound Interest

What is compound interest?

How do I calculate compound interest?

Examiner Tip

Worked example

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Author: Naomi C