True or False? Simple interest is based on the original amount (rather than the current amount).

True. Simple interest is based on the original amount (rather than the current amount). E.g. If you are investing $500 over a period of 3 years, simple interest would be calculated based only on the original $500.

How do you calculate the final balance after simple interest has been earned? E.g. $300 earning 4% simple interest per year for 6 years.

To calculate the final balance after simple interest has been earned, find a percentage (the percentage rate) of the starting amount using a multiplier. Multiply this by the number of time periods (years) it is applied for. Add this on to the starting amount. E.g. (300 × 0.04 × 6) + 300 = 372

True or False? Compound interest is where interest is calculated based on the current amount (rather than the original amount).

True. Compound interest is where interest is calculated based on the current amount (rather than the original amount). E.g. If you are investing $500 over a period of 3 years, compound interest would be calculated on the amount in the account at the end of each time period (including any interest that has been added from previously). Simple interest would always be calculated on the original $500.

True or False? Compound interest is the same as a repeated percentage increase .

True. Compound interest is the same as a repeated percentage increase . E.g. For an investment of £400 with an interest of 3% over a period of 5 years, the final amount can be calculated by finding a 3% increase, five times in a row ( 400 x 1.03 5 ).

True or False? If compound interest is applied to an amount each year, then the amount increases by the same value each year.

False. If compound interest is applied to an amount each year, then the amount does not increase by the same value each year. The amount of interest increases each year. For example, compound interest on $100 at 10% each year, increases by $10 in the first year and then $11 in the second year.

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 ).

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Simple & Compound Interest, Growth & Decay (Cambridge (CIE) IGCSE Maths)

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FrontSimple Interest
True or False?
Simple interest is based on the original amount (rather than the current amount).

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True or False?
Simple interest is based on the original amount (rather than the current amount).
True.
Simple interest is based on the original amount (rather than the current amount).
E.g. If you are investing $500 over a period of 3 years, simple interest would be calculated based only on the original $500.
How do you calculate the final balance after simple interest has been earned?
E.g. $300 earning 4% simple interest per year for 6 years.
To calculate the final balance after simple interest has been earned, find a percentage (the percentage rate) of the starting amount using a multiplier.
Multiply this by the number of time periods (years) it is applied for.
Add this on to the starting amount.
E.g. (300 × 0.04 × 6) + 300 = 372
Given an original amount, the final amount and the rate of simple interest, how can you calculate the number of time periods over which the interest is paid?
E.g. Simple interest is added to an investment of $600 at a rate of 3.5% per year leading to a final amount of $684. For how many years was interest at this rate paid?
Given an original amount, the final amount and the rate of simple interest, you can calculate the number of time periods over which the interest is paid by subtracting the original amount from the final amount (finding the total interest) and dividing the result by the original amount and the rate of simple interest.
E.g. $\frac{684 - 600}{600 \times (\frac{3.5}{100})} = 4$
True or False?
Compound interest is where interest is calculated based on the current amount (rather than the original amount).
True.
Compound interest is where interest is calculated based on the current amount (rather than the original amount).
E.g. If you are investing $500 over a period of 3 years, compound interest would be calculated on the amount in the account at the end of each time period (including any interest that has been added from previously). Simple interest would always be calculated on the original $500.
Compound interest is applied to the amount $P$ at a rate of $r$ % each year. Write down the equation for the amount after $n$ years.
Compound interest is applied to the amount $P$ at a rate of $r$ % for $n$ years. The final amount is found by calculating $P {(1 + \frac{r}{100})}^{n}$ .
True or False?
Compound interest is the same as a repeated percentage increase.
True.
Compound interest is the same as a repeated percentage increase.
E.g. For an investment of £400 with an interest of 3% over a period of 5 years, the final amount can be calculated by finding a 3% increase, five times in a row ( 400 x 1.03⁵).
True or False?
If compound interest is applied to an amount each year, then the amount increases by the same value each year.
False.
If compound interest is applied to an amount each year, then the amount does not increase by the same value each year. The amount of interest increases each year.
For example, compound interest on $100 at 10% each year, increases by $10 in the first year and then $11 in the second year.
How do you calculate the original amount if you are given the final balance after compound interest has been applied?
E.g. Given that the final amount in a savings account after a period of 2 years at an interest rate of 5% is $771.75, find the original investment.
For a reverse percentage problem, you can find the original amount by dividing the final balance by the compounded interest rate.
E.g.
$\begin{array}{rcl} 771.75 & = & P \times {(1 + \frac{5}{100})}^{2} \\ 771.75 & = & P \times 1 . 05^{2} \\ \frac{771.75}{1 . 05^{2}} & = & P \\ P & = & $ 700 \end{array}$
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.
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.
What is the equation used to model exponential growth or decay?
The equation used to model exponential growth or decay is:
- $B = A \times k^{n}$ where:
  $A$ is the starting (initial) amount
  $B$ is the new amount
  $k$ is the appropriate multiplier or scale factor for the growth or decay in the time period
  $n$ is the number of time periods
When using the equation $B = A \times k^{n}$ to model exponential change, what values of $k$ indicate exponential growth?
When using the equation $B = A \times k^{n}$ to model exponential change, if $k > 1$ then it is exponential growth.
True or False?
When using the equation $B = A \times k^{n}$ to model exponential change, a negative value of $k$ indicates exponential decay.
False.
When using the equation $B = A \times k^{n}$ to model exponential change, exponential decay is indicated by $k$ having a value of $0 < k < 1$ .
$k$ cannot have a negative value.

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