Contents:
Percentage Conversion: Are comparisons between numbers. A percentage is a fraction with a particular number divided by 100.
To convert a fraction to a percentage multiply by 100. ie.
x 100 = 100
2 = 50%.
To convert a percentage to a fraction divide by 100. ie. 50% equals 50
Example: Convert
to a percent: Multiply by 100. Equals 100
Example: Convert 75% to a fraction: Divide 75 by 100. This gives a fraction. To show the answer at its lowest terms divide top and bottom by a common factor (25) to give the fraction
.
To find the percentage of a given figure, multiply the given figure by the fraction of the percentage figure divided by 100.
Example: Find 30% of 360. Answer 360 x 30
Increasing / Decreasing: To increase an amount by a certain percentage, first calculate the percentage and add it to the original figure.
Example: Increase £21:50 by 15%. First find 15% of £21:50. 21.5 x 15
225 (two decimal places = £3
Alternative method: The original figure is £21:50 which is 100%. To increase by 15% means that we now want to know what 115% of £21:50 is. Divide 115 by 100 = 1
To decrease an amount by a certain percentage, first calculate the percentage and subtract it from the original figure.
Example: Decrease £21:5 by 15%. As for increasing 15% of 21
Alternative method: The original figure is £21:50 which is 100%. To decrease by 15% means that we now want to know what 85% of £21:50 is. Divide 85 by 100 = 0
One quantity as a percentage of another quantity: To calculate what percentage one figure is of another figure divide the first by the second and multiply by 100.
Example: Find what percentage 60 is of 300 ?
60
Example: Find the percentage profit if item is bought for £5 and sold for £8 ?
The original figure is £5, the profit is therefore £3. (Formula from above: 3
Example: Find the percentage decrease on an item bought for £8 and sold for £5 ?
The original figure is £8, the decrease is therefore £3. (Formula from above: 3
Simple Interest: The initial sum of money invested is the 'principal'. The amount of interest is always calculated on the principal, and while the rate of interest remains the same so does the interest. Simple interest is where the interest is withdrawn at the end of each calculating period ie. each year.
Formula: Simple interest = Rate
Example: Find the simple interest on £1000:00 invested for 9 years at an interest rate of 5%.
Using the Formula: 5/100 x 1000 x 9. (Cancelling zeros) = 5 x10 x 9 = 450 or £450:00. The total sum after 9 years is £1450:00.
Example: Find how many years to accumulate a total sum of £1500:00 if £1000:00 is invested at a simple interest of 5%.
Using the formula and substituting in known values: Simple interest = Rate
Compound Interest: If the interest is not withdrawn until the end of the entire period then compound interest must be calculated. Here the principle increases year on year. This causes a new calculation for each year.
Example: Find the compound interest on £1000:00 invested for 3 years at an interest rate of 5%. Using the formula above but without the time element.
Interest for first year: = 5
Interest for second year: 5
Interest for third year: 5
It is seen that compound interest accumulates quicker than simple interest. Note decimals are rounded to make whole pennies.
Borrowing: Hire purchases and credit purchases can be calculated using the principles above.
Example: An item is bought for £299:99, a deposit of £29:99 was paid and the balance is due over 24 monthly installments of £14:00. With this information it is possible to calculate the following:
The total paid from installments: 24 x £14:00. Equals:£336:00.
The total price including interest: Deposit plus Installments: £29:99 + £336:00. Equals: £365:99.
The total interest: Total price minus Selling price: £365:99 - £299:99. Equals: £66:00.
The flat rate of interest: Total interest divided by amount borrowed multiplied by 100. Amount borrowed is £299:99 - £29:00 = £270:00. Therefore 66
The yearly flat rate of interest is flat rate divided by time. 24
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