Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #51 : Monetary Percentage

Trevor wants to buy a car that costs $4,000. He spends $1,000 of his own money, and borrows the rest from his parents at 6% interest.  What will be the total cost of the car when he finishes paying back the loan?

Possible Answers:

\displaystyle \$4280

\displaystyle \$3180

\displaystyle \$5196

\displaystyle \$4180

\displaystyle \$4360

Correct answer:

\displaystyle \$4180

Explanation:

Trevor needs to pay 6% interest on $3,000 that he is borrowing which amounts to an additional $180, bringing the total cost to $4,180.  

Example Question #18 : How To Find Simple Interest

Tanya opened a credit card with 16% yearly interest to purchase something on sale at a large department store for \displaystyle \$465.99. Unfortunately, she forgot to pay her bill all year. How much will she end up paying for the item if she pays it off now?

Possible Answers:

\displaystyle \$540.55

\displaystyle \$490.65

\displaystyle \$74.56

\displaystyle \$481.99

\displaystyle \$465.99

Correct answer:

\displaystyle \$540.55

Explanation:

When calculating interest on an item you need to multiply the amount of the item by the interest in decimal form. 16% is equivalent to .16.

\displaystyle $465.99*.16=74.56. The second step is to add the interest to the original amount of the item \displaystyle 465.99+74.56, which would give you an answer of \displaystyle \$540.55.

 

You can also solve this problem in one step by multiplying the original price of the item by 1.16. This number means that you are paying for 100% of the item plus the 16% interest. \displaystyle 465.99\times1.16=540.55.

Example Question #61 : Monetary Percentage

Find the simple interest earned if you deposit $2000 into a bank at an annual rate of 5% for 3 years.

Possible Answers:

\displaystyle \$400

\displaystyle \$500

\displaystyle \$200

\displaystyle \$100

\displaystyle \$300

Correct answer:

\displaystyle \$300

Explanation:

To find the simple interest, we use the formula

\displaystyle \text{simple interest} = \text{principal} \cdot \text{rate} \cdot \text{time}

or

\displaystyle SI = P \cdot R \cdot T

where the principal is the initial amount we desposit, the rate is the percentage of interest accruing, and the time is the number of years.

We know

\displaystyle P = \$2000

\displaystyle R = 5\% \ \text{or} \ 0.05

\displaystyle T = 3

So we substitute, and we get

\displaystyle SI = \$2000 \cdot 0.05 \cdot 3

\displaystyle SI = \$300

Therefore, the simple interested earned is $300.

Example Question #12 : How To Find Simple Interest

You deposit $400 at the bank that accrues an interest of 5% every year.  How much interest will you have earned in 10 years?

Possible Answers:

\displaystyle \$50

\displaystyle \$20

\displaystyle \$250

\displaystyle \$45

\displaystyle \$200

Correct answer:

\displaystyle \$200

Explanation:

To find the simple interest accrued, we will use the formula

\displaystyle \text{simple interest} = \text{principal} \cdot \text{rate} \cdot \text{time}

or

\displaystyle \text{simple interest} = P \cdot R \cdot T

We know the following

\displaystyle P = \$400

\displaystyle R = 5\% \ \text{or} \ 0.05

\displaystyle T = 10 \text{ years}

We can substitute into the formula.  We get

\displaystyle \text{simple interest} = \$400 \cdot 0.05 \cdot 10

\displaystyle \text{simple interest} = \$200

Therefore, the amount of interest earned is $200.

Example Question #21 : How To Find Simple Interest

You deposit $2000 in a bank that earns 12% interest every year.  How much interest will accrue in 5 years?

Possible Answers:

\displaystyle \$1200

\displaystyle \$240

\displaystyle \$1000

\displaystyle \$60

\displaystyle \$600

Correct answer:

\displaystyle \$1200

Explanation:

To find the interest earned, we use the following formula

\displaystyle \text{simple interest} = P \cdot R \cdot T

where P is the principal or amount deposited, R is the rate of interest earned, and T is the time in years.  Using this formula, we can substitute.  We get

\displaystyle \text{simple interest} = \$2000 \cdot 12\% \cdot 5

\displaystyle \text{simple interest} = \$2000 \cdot 0.12 \cdot 5

\displaystyle \text{simple interest} = \$1200

Therefore, the amount of interested earned after 5 years is $1200.

Example Question #22 : How To Find Simple Interest

You deposit $1500 into a savings account.  The account earns 7% in interest annualy.  How much simple interest will you earn in 6 years?

Possible Answers:

\displaystyle \$630

\displaystyle \$420

\displaystyle \$63

\displaystyle \$42

\displaystyle \$6300

Correct answer:

\displaystyle \$630

Explanation:

To find simple interest, we use the following formula:

\displaystyle \text{simple interest} = P \cdot R \cdot T

where

\displaystyle P = \text{principal or amount deposited}

\displaystyle R = \text{percentage rate}

\displaystyle T = \text{time in years}

 

Given what we know

\displaystyle P = \$1500

\displaystyle R = 7\% \text{ or } 0.07

\displaystyle T = 6 \text{ years}

we can substitute into the formula.  We get

\displaystyle \text{simple interest} = \$1500 \cdot 0.07 \cdot 6

\displaystyle \text{simple interest} = \$630

 

Therefore, you earned a total of \displaystyle \$630 in simple interest.

Example Question #23 : How To Find Simple Interest

You deposit $400 into a savings account.  The account earns 3% interest per year.  How much simple interest will you earn after 4 years?

Possible Answers:

\displaystyle \$120

\displaystyle \$48

\displaystyle \$100

\displaystyle \$480

\displaystyle \$300

Correct answer:

\displaystyle \$48

Explanation:

To find simple interest, we use the following formula:

\displaystyle \text{simple interest} = P \cdot R \cdot T

where

\displaystyle P = \text{principal or amount deposited}

\displaystyle R = \text{percentage rate}

\displaystyle T = \text{time in years}

 

Given what we know

\displaystyle P = \$400

\displaystyle R = 3\% \text{ or } 0.03

\displaystyle T = 4 \text{ years}

we can substitute into the formula.  We get

\displaystyle \text{simple interest} = \$400 \cdot 0.03 \cdot 4

\displaystyle \text{simple interest} = \$48

 

Therefore, you earned a total of \displaystyle \$48 in simple interest.

Example Question #61 : Monetary Percentage

You invest $550 in a savings account that accrues interest at a rate of 6% annually. How much interest will you earn after 3 years?

Possible Answers:

\displaystyle \$33

\displaystyle \$99

\displaystyle \$990

\displaystyle \$11

\displaystyle \$330

Correct answer:

\displaystyle \$99

Explanation:

To find simple interest, we use the following formula:

\displaystyle \text{simple interest} = P \cdot R \cdot T

where

\displaystyle P = \text{principal or amount deposited}

\displaystyle R = \text{percentage rate}

\displaystyle T = \text{time in years}

 

Given what we know

\displaystyle P = \$550

\displaystyle R = 6\% \text{ or } 0.06

\displaystyle T = 3 \text{ years}

we can substitute into the formula.  We get

\displaystyle \text{simple interest} = \$550 \cdot 0.06 \cdot 3

\displaystyle \text{simple interest} = \$99

 

Therefore, you earned a total of \displaystyle \$99 in simple interest.

Example Question #62 : Monetary Percentage

You deposit $700 in a savings account at a bank.  It accrues 4% interest annually.  How much simple interest will you earn after 2.5 years?

Possible Answers:

\displaystyle \$56

\displaystyle \$112

\displaystyle \$28

\displaystyle \$70

\displaystyle \$280

Correct answer:

\displaystyle \$70

Explanation:

To find simple interest, we use the following formula:

\displaystyle \text{simple interest} = P \cdot R \cdot T

where

\displaystyle P = \text{principal or amount deposited}

\displaystyle R = \text{percentage rate}

\displaystyle T = \text{time in years}

 

Given what we know

\displaystyle P = \$700

\displaystyle R = 4\% \text{ or } 0.04

\displaystyle T = 2.5 \text{ years}

we can substitute into the formula.  We get

\displaystyle \text{simple interest} = \$700 \cdot 0.04 \cdot 2.5

\displaystyle \text{simple interest} = \$70

 

Therefore, you earned a total of \displaystyle \$70 in simple interest.

Example Question #24 : How To Find Simple Interest

Joey received a savings bond that pays out 4% interest each year. The face value of the bond is $500. How much will Joey receive after holding the bond for one year?

Possible Answers:

\displaystyle \$200

\displaystyle \$0.40

\displaystyle \$20

\displaystyle \$4

\displaystyle \$40

Correct answer:

\displaystyle \$20

Explanation:

Convert 4% into a decimal...

4% = 0.04

...and multiply by the face value of the bond. If \displaystyle x is the interest paid after one year, the equation would look like this:

\displaystyle x=500\times0.04

\displaystyle x=20

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