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3.2 Solve percent applications  (Page 4/18)

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Find the percent decrease. (Round to the nearest tenth of a percent.)

The population of North Dakota was about 672,000 in 2010. The population is projected to be about 630,000 in 2020.

6.3%

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Find the percent decrease.

Last year, Sheila’s salary was $42,000. Because of furlough days, this year, her salary was $37,800.

10%

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Solve simple interest applications

Do you know that banks pay you to keep your money? The money a customer puts in the bank is called the principal    , P , and the money the bank pays the customer is called the interest    . The interest is computed as a certain percent of the principal; called the rate of interest    , r . We usually express rate of interest as a percent per year, and we calculate it by using the decimal equivalent of the percent. The variable t , (for time ) represents the number of years the money is in the account.

To find the interest we use the simple interest formula, I = P r t .

Simple interest

If an amount of money, P , called the principal, is invested for a period of t years at an annual interest rate r , the amount of interest, I , earned is

I = P r t where I = interest P = principal r = rate t = time

Interest earned according to this formula is called simple interest    .

Interest may also be calculated another way, called compound interest. This type of interest will be covered in later math classes.

The formula we use to calculate simple interest is I = P r t . To use the formula, we substitute in the values the problem gives us for the variables, and then solve for the unknown variable. It may be helpful to organize the information in a chart.

Nathaly deposited $12,500 in her bank account where it will earn 4% interest. How much interest will Nathaly earn in 5 years?

I = ? P = $12,500 r = 4 % t = 5 years

Solution

Step 1. Read the problem. Step 2. Identify what we are looking for. the amount of interest earned Step 3. Name what we are looking for. Choose a variable to represent that quantity Let I = the amount of interest. Step 4. Translate into an equation. Write the formula. I = P r t Substitute in the given information. I = ( 12,500 ) ( .04 ) ( 5 ) Step 5. Solve the equation. I = 2,500 Step 6. Check : Does this make sense? Is $2,500 is a reasonable interest on $12,500? Yes. Step 7. Answer the question with a complete sentence. The interest is $2,500.

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Areli invested a principal of $950 in her bank account with interest rate 3%. How much interest did she earn in 5 years?

$142.50

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Susana invested a principal of $36,000 in her bank account with interest rate 6.5%. How much interest did she earn in 3 years?

$7,020

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There may be times when we know the amount of interest earned on a given principal over a certain length of time, but we don’t know the rate. To find the rate, we use the simple interest formula, substitute in the given values for the principal and time, and then solve for the rate.

Loren loaned his brother $3,000 to help him buy a car. In 4 years his brother paid him back the $3,000 plus $660 in interest. What was the rate of interest?

I = $660 P = $3,000 r = ? t = 4 years

Solution

Step 1. Read the problem. Step 2. Identify what we are looking for. the rate of interest Step 3. Name what we are looking for. Choose a variable to represent that quantity . Let r = rate of interest. Step 4. Translate into an equation. Write the formula. Substitute in the given information. Step 5. Solve the equation. Divide. Change to percent form. I = P r t 660 = ( 3,000 ) r ( 4 ) 660 = ( 12,000 ) r 0.055 = r 5.5 % = r Step 6. Check : Does this make sense? I = P r t 660 = ? ( 3,000 ) ( 0.055 ) ( 4 ) 660 = 660 ✓ Step 7. Answer the question with a complete sentence. The rate of interest was 5.5%.

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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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