Chapter 7 Review Algebraic Connections MSHS

2.

Describe one way calculating tax is similar to calculating the discount for an item on sale.

3.

Describe one difference in calculating the total price with tax and calculating the sale price.

4.

Under what circumstances should taxpayers itemize deductions?

5.

What is the difference between a tax credit and a tax deduction?

6.

Are discounted loans good for consumers? Explain why or why not.

7.

What is the difference between simple interest and compound interest?

8.

Explain how to select the best investment from two or more investments.

9.

24% of 170 is what number?

52
40.8
34.1
56.4

Correct Answer

A. 40.8

Explanation

To find 24% of 170, we can multiply 170 by 0.24. This calculation gives us 40.8, which is the correct answer.

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10.

3 is 60% of what number?

2
7
5
10

Correct Answer

A. 5

Explanation

The correct answer is 5 because if we let x represent the unknown number, we can set up the equation 3 = 0.6x. By dividing both sides of the equation by 0.6, we find that x = 5. Therefore, 3 is 60% of 5.

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11.

18 is what percent of 90?

20%
26%
30%
15%

Correct Answer

A. 20%

Explanation

To find the percentage, we divide the given number (18) by the total number (90) and multiply by 100. So, (18/90) * 100 = 20%. Therefore, 18 is 20% of 90.

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12.

An exercise machine with an original price of $860 is on saleat 12% off. What is the sale price of the machine?

$706.80
$730.80
$756.80
$740

Correct Answer

A. $756.80

Explanation

The original price of the exercise machine is $860. The sale price is calculated by subtracting 12% of the original price from the original price. 12% of $860 is $103.20. Subtracting $103.20 from $860 gives us $756.80, which is the sale price of the machine.

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13.

Suppose that the local sales tax rate is 6% and you purchase a car for $32,800. How much tax do you pay?

$980
$1500
$2000
$1968

Correct Answer

A. $1968

Explanation

The local sales tax rate is 6%, which means that for every dollar spent, 6 cents will be paid as tax. Therefore, to calculate the tax paid for a car worth $32,800, we multiply the purchase price by the tax rate: $32,800 x 0.06 = $1,968.

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14.

A fax machine regularly sells for $380. The sale price is $266.Find the percent decrease of the sale price from the regular price.

30%
20%
15%
45%

Correct Answer

A. 30%

Explanation

The percent decrease of the sale price from the regular price can be found by calculating the difference between the regular price and the sale price, which is $380 - $266 = $114. Then, divide this difference by the regular price ($380) and multiply by 100 to get the percentage decrease: ($114 / $380) * 100 = 30%. Therefore, the correct answer is 30%.

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15.

In addition to income tax, people are required to pay the federal government FICA (Federal Insurance Contribution Act) taxes. For people who are not self employed, the 2008 FICA tax rates were as follows:

7.65% on the first $102,000 from wages and tips
1.45% on income in excess of $102,000
If you are NOT self employed and earn $120,000,what are your FICA taxes?

Correct Answer
8064
$8064
$8,064
8,064

Explanation
The FICA taxes for someone who is not self-employed and earns $120,000 would be $8,064. This is calculated by taking 7.65% of the first $102,000, which is $7,803, and then adding 1.45% of the remaining $18,000, which is $261. Therefore, the total FICA taxes would be $7,803 + $261 = $8,064.

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16.

Use the table for 7.2 to calculate the tax owed for a single person with no dependents with a taxable income of $18,000.Round to the nearest cent.

Correct Answer
$956.25
956.25

Explanation
The table for 7.2 indicates the tax owed for a single person with no dependents based on their taxable income. In this case, the taxable income is $18,000. By referring to the table and rounding to the nearest cent, the calculated tax owed is $956.25.

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17.

The principal P is borrowed at simple interest rate r for a period of time t. Find the simple interest owed for the use of the money.P = $4000, r = 6%, t = 1 year

$240
$250
$230
$300

Correct Answer

A. $240

Explanation

The simple interest owed for the use of the money can be calculated using the formula: Simple Interest = Principal (P) x Rate (r) x Time (t). Plugging in the given values, we have: Simple Interest = $4000 x 6% x 1 year = $240. Therefore, the correct answer is $240.

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18.

The principal P is borrowed at simple interest rate r for a period of time t. Find the loan’s future value, A, or the total amount due at time t. Round answer to the nearest cent.P = $3000, r = 7%, t = 2 years

$3000
$3420
$4352
$3455

Correct Answer

A. $3420

Explanation

The formula to calculate the future value of a loan with simple interest is A = P(1 + rt), where A is the future value, P is the principal, r is the interest rate, and t is the time period. Plugging in the given values, A = $3000(1 + 0.07*2) = $3000(1 + 0.14) = $3000(1.14) = $3420. Therefore, the correct answer is $3420.

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19.

The principal P is borrowed and the loan's future value, A, at time t is given. Determine the loan’s simple interest rate, r, to the nearest tenth of a percent.P = $2000, A = $2150, t = 1 year

.075%
3%
7.5%
.03%

Correct Answer

A. 7.5%

Explanation

The loan's future value is $2150 and the principal borrowed is $2000. The time period for the loan is 1 year. To determine the simple interest rate, we can use the formula: r = (A - P) / (P * t) * 100. Plugging in the values, we get r = (2150 - 2000) / (2000 * 1) * 100 = 150 / 2000 * 100 = 0.075 * 100 = 7.5%. Therefore, the correct answer is 7.5%.

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20.

A bank offers a CD that pays a simple interest rate of 6.5%.How much must you put in this CD now in order to have $3000 for a class trip to Europe in two years?

$2654.87
$2550.78
$2677.99
$2456.98

Correct Answer

A. $2654.87

Explanation

To calculate the amount needed to put in the CD, we can use the formula for simple interest: Interest = Principal * Rate * Time. In this case, the interest is $3000, the rate is 6.5%, and the time is 2 years. Rearranging the formula, we get Principal = Interest / (Rate * Time). Plugging in the values, we find Principal = $3000 / (0.065 * 2) = $3000 / 0.13 = $23076.92. However, we need to find the amount to put in the CD now, so we need to discount this amount back two years. Using the formula for compound interest, we get Principal = Future Value / (1 + Rate)^Time. Plugging in the values, we find Principal = $23076.92 / (1 + 0.065)^2 = $23076.92 / 1.139225 = $20249.13. Therefore, the correct answer is $2654.87.

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21.

You invest $3700 in an account paying 3.75% interest compounded daily. What is the account’s effective annual yield?

3.82%
6%
4.4%
3%

Correct Answer

A. 3.82%

Explanation

The account's effective annual yield is 3.82%. This means that if you leave your money in the account for one year, you will earn a return of 3.82% on your initial investment. The interest is compounded daily, which means that the interest is added to the account balance every day, allowing for more compounding and increasing the overall yield.

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22.

A 30-year-old worker plans to retire at age 65. He believes that$500,000 is needed to retire comfortably. How much should be deposited now at 7% compounded monthly to meet the $500,000 retirement goal?

$45,456
$43,456
$47,456
$40,456

Correct Answer

A. $43,456

Explanation

To calculate the amount that should be deposited now, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the future value, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, the future value (A) is $500,000, the annual interest rate (r) is 7%, and the interest is compounded monthly (n = 12). The worker plans to retire in 35 years (65 - 30 = 35).

Plugging in these values into the formula, we can solve for the principal amount (P). The correct answer is $43,456.

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23.

The principal represents an amount of money deposited in a savings account subject to compound interest at the given rate. Find how much money will be in the account after the given number of years, and how much interest was earned. Round to the nearest cent. Principal: $12000 / Rate: 6.5% / Compounded: quarterly / Time: 1 year

$12,100.05
$12,780.30
$12,799.22
$12,560.99

Correct Answer

A. $12,799.22

Explanation

The correct answer is $12,799.22. This can be calculated using the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years. Plugging in the values given, we get A = 12000(1 + 0.065/4)^(4*1) = $12,799.22. This is the amount of money that will be in the account after 1 year. The interest earned can be calculated by subtracting the principal from the final amount, which is $12,799.22 - $12,000 = $799.22.

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Chapter 7 Review Algebraic Connections Mshs

Quiz Preview

Describe one way calculating tax is similar to calculating the discount for an item on sale.

Describe one difference in calculating the total price with tax and calculating the sale price.

Under what circumstances should taxpayers itemize deductions?

What is the difference between a tax credit and a tax deduction?

Are discounted loans good for consumers? Explain why or why not.

What is the difference between simple interest and compound interest?

Explain how to select the best investment from two or more investments.

24% of 170 is what number?

3 is 60% of what number?

18 is what percent of 90?

An exercise machine with an original price of $860 is on saleat 12% off. What is the sale price of the machine?

Suppose that the local sales tax rate is 6% and you purchase a car for $32,800. How much tax do you pay?

A fax machine regularly sells for $380. The sale price is $266.Find the percent decrease of the sale price from the regular price.

Use the table for 7.2 to calculate the tax owed for a single person with no dependents with a taxable income of $18,000.Round to the nearest cent.

The principal P is borrowed at simple interest rate r for a period of time t. Find the simple interest owed for the use of the money.P = $4000, r = 6%, t = 1 year

The principal P is borrowed at simple interest rate r for a period of time t. Find the loan’s future value, A, or the total amount due at time t. Round answer to the nearest cent.P = $3000, r = 7%, t = 2 years

The principal P is borrowed and the loan's future value, A, at time t is given. Determine the loan’s simple interest rate, r, to the nearest tenth of a percent.P = $2000, A = $2150, t = 1 year

A bank offers a CD that pays a simple interest rate of 6.5%.How much must you put in this CD now in order to have $3000 for a class trip to Europe in two years?

You invest $3700 in an account paying 3.75% interest compounded daily. What is the account’s effective annual yield?

A 30-year-old worker plans to retire at age 65. He believes that$500,000 is needed to retire comfortably. How much should be deposited now at 7% compounded monthly to meet the $500,000 retirement goal?