Maths Descriptions

1) To Calculate Compound Interest:

Meaning of Words

Interest: Is the money you pay to the bank when borrowing money from them. It can also be the money the bank pays you for keeping your money. It is calculated by multiplying the rate by the balance.

Rate: A percentage (e.g. 4%, 9.6%, 11%) used to calculate interest.

Balance: The amount of money a person has in a bank account. It is usually called the "Principal".

Compound Interest: Interest calculations made during a given period when money earns interest on top of the original calculated balances during that period at given intervals. (e.g. look at the example below)

To calculate compound interest annually: The annual interest is divided by the given intervals, then the first interval and every successive interval is multiplied by that rate and added to the new balance at every interval. (See the example below)

Example...
A person borrows $320 at 13.5% p.a. compounded monthly for 1 year. What will be the balance after 12 months?

13.5% ÷ 12 months = 1.125%, which is the rate for 1 month.


Principal for 1st month = $320 Original Balance = $320.00
Interest for 1st month = 1.125% of $320 $320.00 ×1.125% = $3.60
= $3.60
Principal for 2nd month = $323.60 $320.00 + $3.60 = $323.60
Interest for 2nd month = 1.125% of $323.60 $323.60 ×1.125% = $3.64
= $3.64
Principal for 3rd month = $327.24 $323.60 + $3.64 = $327.24
Interest for 3rd month = 1.125% of $327.24 $327.24×1.125% = $3.68
= $3.68
Principal for 4th month = $330.92 $327.24 + $3.68 = $330.92
Interest for 4th month = 1.125% of $330.92 $330.92 ×1.125% = $3.72
= $3.72
Principal for 5th month = $334.64 $330.92 + $3.72 = $334.64
Interest for 5th month = 1.125% of $334.64 $334.64 ×1.125% = $3.76
= $3.76
Principal for 6th month = $338.40 $334.64 + $3.76 = $338.40
Interest for 6th month = 1.125% of $338.40 $338.40 ×1.125% = $3.81
= $3.81
Principal for 7th month = $342.21 $338.40 + $3.81 = $342.21
Interest for 7th month = 1.125% of $342.21 $342.21 ×1.125% = $3.85
= $3.85
Principal for 8th month = $346.06 $342.21 + $3.85 = $346.06
Interest for 8th month = 1.125% of $346.06 $346.06 ×1.125% = $3.89
= $3.89
Principal for 9th month = $349.95 $346.06 + $3.89 = $349.95
Interest for 9th month = 1.125% of $349.95 $349.95 ×1.125% = $3.94
= $3.94
Principal for 10th month = $353.89 $349.95 + $3.94 = $353.89
Interest for 10th month = 1.125% of $353.89 $353.89 ×1.125% = $3.98
= $3.98
Principal for 11th month = $357.87 $353.89 + $3.98 = $357.87
Interest for 11th month = 1.125% of $357.87 $357.87 ×1.125% = $4.03
= $4.03
Principal for 12th month = $361.90 $357.87 + $4.03 = $361.90

Quick Way: 320 × (1 + 0.01125)11 = $361.90

Principal = $320
Rate = 1.125% or 0.01125 (1.125/100) interest charged each month.
Number of months times the rate is to be squared: 11 times (12 months - 1), because the first month has already been calculated.

Formula: C = P × (1 + R)n - 1


C = Compound Interest
P = Principal (balance)
R = Rate (%)
n = Time (e.g. in the example above it would be 11)

2) To Find the Surface Area of a Cube:

Multiply the length of one side by itself then multiply the result by six because there are six sides to a cube and all sides are equal.

Formula: SA = L2 × 6

SA = surface area.

L = length

Example...

A cube has a length measurement of 4 cm. Find the surface area.

42 × 6 = 96 cm2, is the surface area

To Find the Volume of a Cube:

Find the area of one side of the cube, then multiply the result by itself three times.

Formula: V = L3

V = volume

L = length

Example...

A cube has a length measurement of 4 cm. Find the volume.

V = 43 

4 × 4 × 4 = 64 

V = 64 cm²

3) A sequence is an ordered set of numbers. In this example the formula will be worked out by finding the unique sequence, then filling in the next five numbers of the sequence.

Example:

Find the next five terms of the following sequence...

43, 50, 57.....

Answer: 64, 71, 78, 85, 92

43 + 7 = 50, 50 + 7 = 57, 57 + 7 = 64 ...

4) To work out tables, calculate each vertical column equation by the value of x in every horizontal cell.

Substitute: Is to replace a number by a variable or to replace a variable by a number.

Example... (answers are in red)


Substitute

x + 6

2 - x

4x - 5

x2

3 - 2x

x = 2

8

0 3 4 -1

x = 7

13 -5 23 49 -11

5) How to find the area of an octagon:

Meaning of words

An octagon is a polygon having eight sides.
A
polygon is a closed plain figure bounded by three or more straight sides that meet in pairs in the same number of vertices and do not intersect other than at these vertices.
Vertices is the plural of vertex.
Vertex means the point opposite the base of a figure or the point of intersection of two sides of a plain figure or angle.

Different methods or formulas are used for calculating the area of polygons. The following method is used for calculating the area of an octagon.

Formula: 2 × r2× 1.4142135 (the last number is the square root of 2)

r = radius

The radius is a straight line from the centre to any point on the outside of the shape.

Find the radius of the octagon, then perform the formula.
e.g. if the radius of an octagon was 4 cm, then 2 × 42× 1.4142135 = 45.25 cm2, which is the area.

6) A prime number is any integer which can only be divided by itself and one.

An integer is any number which does not have a decimal place. It can be a negative number (e.g. -5, -7, -3) or positive number (e.g. 5, 7, 3).

e.g. 1, 2, 3, 5, 7, 11, 13 are prime numbers.

7) To calculate the interest on a borrowing: multiply the principal by the rate, then multiply the result by the amount of years the loan is taken out.

Meaning of words.

Interest: Is a percentage of money paid to the bank when borrowing money from that bank it is calculated by multiplying the rate by the balance.

Rate: Is a percentage (e.g. 4%, 9.6%, 11%) used to calculate interest.

In this case the explanation of the balance is the following: the amount of money owed to the bank at any given time. It is usually called the "principal amount owed".

Example:

Stan borrowed $12 000 at 12.68% p.a. for 3 years. Find the total amount he owes on top of what he has already borrowed.

($12 000 × 12.68%) × 3 = $4 564.80, this is the total interest charged.

$12 000 + $4 564.80 = $16 564.80, this is the amount owed.

Amount owed: $16 564.80

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