Percentage
A percentage is a ratio expressed as a fraction with denominator 100. It is often denoted as:
$\frac{25}{100}$ = 0,25 = 25%
In order to turn any fraction into a percentage, we have to multiply the numerator and the denominator by the same number, so that the product in the denominator is 100. For example:
$\frac{3}{20}$ = $\frac{3}{20}*\frac{5}{5}$ = $\frac{15}{100}$ = 15%
In real life situations, percentages are computed by dividing the part by the whole. For example, if a person eats 2 candies out of a package with 8 candies, the percentage he or she ate is given by:
$\frac{2}{8}$ = $\frac{2}{8}*\frac{12.5}{12.5}$ = $\frac{25}{100}$ = 25%
Interest Rate
Interest rate is the amount due as a proportion of the amount lent (or deposited, borrowed).
The interest rate can be either simple or compound.
It is simple when the interest is computed by multiplying the rate by the principal and by the number of periods.
For example, if one makes an investment of US200,000 at 1% simple monthly interest rate:
After one month the interest added is US2,000;
In the second month the interest added is again US2,000;
The same goes in the third, fourth,... months: the interest added monthly will always be US2,000, that is, 1% of the initial principal.
After 5 months, for example, the balance of such investment will be US210,000 (the initial principal, US200,000, plus 5 times the US2,000 monthly interest).
If the rate is compounded, the monthly interest is computed on the initial principal plus all of the accumulated interest of previous periods.
For example, if one makes an investment of US200,000 at 1% compounding monthly interest rate:
After one month the interest added is US2,000;
In the second month the interest added is US2,020 (1% of US202,000);
In the third month the interest added is US2,040 (1% of US204,020);
In the fourth month the interest added is US2,060 (1% of US206,060);
In the fifth month the interest added is US2,081 (1% of US208,120);
After 5 months, the balance of such investment will be US210,202.
The balance of the investment with compounding interest rate is a little greater than that with simple interest rate, because the compounding interest is computed including the interest accumulated in all previous periods.
Profit Margin
Profit margin is a ratio that indicates how many cents of profit one makes for each dollar invested or for each dollar of sale.
For example, if one buys a house for US200,000, and sells it for US240,000, the profit was US40,000. The profit margin was
$\frac{40,000}{200,000}$ = 20%:
If Apple reports that it achieved a 25% profit margin on the sales of iPhones, it means that an iPhone that is sold for US1,000 generates a profit of US250.
Solved SAT Practice Tests
Find Practice Tests in the following links:
SAT Practice Tests - Percentage, Interest Rate, and Profit Margin
Additional Practice Tests - Percentage, Interest Rate, and Profit Margin
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