Define simple interest .

Simple interest is interest worked out only on the starting amount , however long the money is left there. Interest itself is money that is added at regular intervals, which increases savings and increases a debt.

True or False? With simple interest , the amount earned each year gets bigger as the years go by.

False. Every year's interest is the same size, because it is always the same percentage of a starting amount that never changes.

Define compound interest .

Compound interest is interest worked out on the running total rather than on the starting amount. Each period's interest is added on before the next period's interest is worked out.

Define the term depreciation .

Depreciation is where an item loses value over time.

True or False? Depreciation is the same as a repeated percentage decrease .

True. Depreciation is the same as a repeated percentage decrease . E.g. For an item with an original value of £200 that depreciates in value by 4% each year over a period of 6 years, its value at the end of 6 years can be calculated by finding a 4% decrease, six times in a row ( 200 x 0.96 6 ).

GCSEMathsEdexcelFoundationFlashcardsNumberSimple & Compound Interest, Growth & Decay

Simple & Compound Interest, Growth & Decay (Edexcel GCSE Maths: Foundation): Flashcards

Exam code: 1MA1

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FrontSimple Interest
Define simple interest.

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Cards in this collection (16)

Define simple interest.
Simple interest is interest worked out only on the starting amount, however long the money is left there.
Interest itself is money that is added at regular intervals, which increases savings and increases a debt.
A bank pays simple interest of $4 %$ per year, and $4 %$ of £250 is £10. Complete the working for the total interest earned over $6$ years:
$10 \times______=______$
The completed working is:
$10 \times 6 = 60$
The yearly interest is multiplied by the number of years, so £60 of interest is earned.
Once you know the total simple interest earned, how do you find the total amount in the account?
Add the interest on to the starting amount.
With £250 invested and £60 of interest earned, the account holds $250 + 60 = 310$ , so £310.
£9000 earns simple interest for $5$ years and grows to £11 700. How do you find the yearly percentage rate?
Find the total interest, $11700 - 9000 = 2700$ , and divide it by the number of years to get $2700 \div 5 = 540$ each year.
Then write that as a percentage of the starting amount: $\frac{540}{9000} = 0.06$ , so the rate is $6 %$ .
True or False?
With simple interest, the amount earned each year gets bigger as the years go by.
False.
Every year's interest is the same size, because it is always the same percentage of a starting amount that never changes.
Define compound interest.
Compound interest is interest worked out on the running total rather than on the starting amount.
Each period's interest is added on before the next period's interest is worked out.
£100 earns $10 %$ compound interest a year. What is the balance at the end of each of the first three years?
It reaches £110, then £121, then £133.10.
Notice that the interest added rises from £10 to £11 to £12.10 as the years go by.
How do you increase £300 by $5 %$ each year for $3$ years in one calculation?
Apply the multiplier once for each year, which is the same as raising it to that power:
$300 \times 1 . 05^{3}$
The same works for any number of years, so $12$ years would use $1 . 05^{12}$ .
Complete the compound interest formula, in which $P$ is the starting amount, $r$ is the percentage rate and $n$ is the number of years:
$final balance = P {(1 + \frac{______}{______})}^{______}$
The completed formula is:
$final balance = P {(1 + \frac{r}{100})}^{n}$
The bracket works out to the same value as the multiplier, so $15 %$ gives $1.15$ .
Does $2000 \times 1 . 04^{12}$ give the interest earned or the total balance?
A calculation like this gives the total balance at the end of the $12$ years, which is £3202.06, not the interest earned.
To find the interest on its own, subtract the starting amount: $3202.06 - 2000 = 1202.06$ .
True or False?
Over several years, compound interest earns more than simple interest at the same rate.
True.
£500 at $6 %$ is worth £595.51 after three years with compound interest, against £590 with simple interest at the same rate.
Define the term depreciation.
Depreciation is where an item loses value over time.
An item that initially had a value of $P$ depreciates at a rate of $r$ % each year. Write down the equation for the value of the item after $n$ years.
An item that initially had a value of $P$ depreciates at a rate of $r$ % each year. After $n$ years the value of the item can be found by calculating $P {(1 - \frac{r}{100})}^{n}$ .
True or False?
Depreciation is the same as a repeated percentage decrease.
True.
Depreciation is the same as a repeated percentage decrease.
E.g. For an item with an original value of £200 that depreciates in value by 4% each year over a period of 6 years, its value at the end of 6 years can be calculated by finding a 4% decrease, six times in a row ( 200 x 0.96⁶).
True or False?
When a quantity grows exponentially it is increasing from an original amount by a percentage each year for $n$ years.
True.
When a quantity grows exponentially it is increasing from an original amount by a percentage each year for $n$ years.
Bacterial growth is an example of exponential growth.
(Note that other time periods are possible, i.e. seconds, hours, days, etc., instead of years.)
What is exponential decay?
When a quantity exponentially decays it is decreasing from an original amount by a percentage each year for $n$ years.
The temperature of hot water cooling down is an example of exponential decay.
(Note that other time periods are possible, i.e. seconds, hours, days, etc., instead of years.)

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