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# Algebra Percents and Simple Interest Study Guide (page 2)

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Updated on Oct 3, 2011

#### Example

After a 68% decrease, a value is now 74. What was the original value?

Let x represent the original value. The difference between the original value and the new value is x – 74. Divide that by the original value, x, and set it equal to the percent decrease, 68%, which is 0.68:

Multiply both sides of the equation by x, and then subtract x from both sides:

0.68x = x – 74

–0.32x = –74

Divide both sides by –0.32:

x = 231.25

## Simple Interest

We can find how much interest an amount of money, or principal, has gained by multiplying the principal by an interest rate and a length of time. The formula for interest is I = prt. Interest, principal, rate, and time are all variables, and given any three of them, we can substitute those values into the equation to find the missing fourth value.

Example

If a principal of \$500 gains \$60 in interest in three years, what was the interest rate per year?

The interest rate is the percent of the principal that is added as interest each year. Because I = prt and we are looking for the rate, r, we can divide both sides of the equation by pt to get r alone on the right side:

.

To find the rate, divide the interest by the product of the principal and the time: 60 ÷ (500)(3) = 60 ÷ 1,500 = 0.04 = 4%. The principal gained interest at a rate of 4% per year.

#### Tip:

When calculating interest, be sure the interest rate and the time have consistent units of measure. If the interest rate is given on a yearly basis, the time must also be in years. If the interest rate is given on a yearly basis and the time is given in months, convert the time to years before using the interest formula.

#### Example

If \$36 in interest is gained over six months at a rate of 6% per year, how much was the principal?

We can rewrite the formula I = prt to solve for p by dividing both sides of the equation by rt: . The interest rate is given per year, but the length of time is given in months. Divide the number of months by 12, because there are 12 months in a year: 6 ÷ 12 = 0.5. The time is 0.5 years and the rate is 6%, or 0.06. Because \$1,200. The principal was \$1,200.

Find practice problems and solutions for these concepts at Algebra Percents and Simple Interest Practice Questions.

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