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Do you remember what “interest” is in the monetary world of saving and borrowing? Interest is the amount of extra money you earn or you have to pay back. On savings, you earn, while on loans and credit, such as credit cards, you pay back. Both are paid on the base value of what was saved or loaned. This base value is known as the principal.

There are two basic forms of interest, i.e., simple interest and compound interest. For this quiz you will only be dealing with compound interest.

What is compound interest?

Well first let’s refresh on what simple interest is. The formula to calculate simple interest is I = PRT (interest equals principal, interest rate and time). In essence, when you receive simple interest you only earn or pay interest on the principal balance. So if you had $10,000.00 in savings and it earns 4% interest each year, no matter what month it is in, you are still only earning interest on the $10,000.00 even if the amount in the account is now $10,140.00 with $140.00 being interest earned to date. This is a good thing but compound interest is even better. Why?

With compound interest you not only earn interest on the principal balance but you also earn interest on the interest earnings. In order to calculate compound interest we have a new formula to follow. It is: **A = P(1 + r) ^{t}**.

A = The amount of money (including the accrued interest) after __ years/months or the compound amount

P = The principal saved or owed

r = The interest rate earned per year

t = The time period of the loan or amount saved (notice that the time is put into the “power” position)

So let’s use some real numbers here. You are going to borrow $500.00 at an interest rate of 2.65% for 2 years. Using the compound interest formula that will read as follows:

A = 500(1 + .0265)^{2}

500(1.0265)^{2}

(1.0265 x 1.0265 = 1.054)

500 x 1.054 = 527

$27.00 is the compound interest over two years and

A = $527.00 as the full amount that will have to be paid back over the two years.

Okay, let’s tackle the next ten problems. For each problem find out how much compound interest will need to be paid or earned and how much in total will be paid back or will be in savings. *(Round decimals to the nearest 100th.)*

1.

Farmer Richards purchased two new tractors for his farm. He had to borrow $312,000.00 at an interest rate of 3.75%, compounded annually. He took out a 6 year loan. How much compound interest to the nearest rounded 100th will accrue over the 6 years and what will be the full amount that Farmer Richards will have to pay back?

Compound Interest Accrued: $75,000.00; Full Amount to Pay-Off Loan: $387,000.00

Compound Interest Accrued: $77,000.00; Full Amount to Pay-Off Loan: $389,000.00

Compound Interest Accrued: $78,000.00; Full Amount to Pay-Off Loan: $390,000.00

Compound Interest Accrued: $81,000.00; Full Amount to Pay-Off Loan: $393,000.00

2.

Amanda has $75.00 in the bank which is earning 8% interest, compounded annually. If she does not touch this account, how much compound interest will she earn in 1 year and what will be the new amount of her bank account?

Compound Interest Earned: $7.50; Amount in Savings: $82.50

Compound Interest Earned: $7.00; Amount in Savings: $82.00

Compound Interest Earned: $6.50; Amount in Savings: $81.50

Compound Interest Earned: $6.00; Amount in Savings: $81.00

The compound formula is A = P(1 + r)^{t}. Substituting the letters for numbers we get:

75(1 + .08)^{1}

(1 + .08)^{1} = (1.08)

75 x 1.08 = $81 (is the amount in her account after 1 year)

$81.00 - $75.00 = $6.00 (is the compound interest earned over 1 year)

__Solution__: Amanda will earn $6.00 in compound interest in 1 year and the full amount in her bank account will be $81.00.

Answer (d) is the correct answer

75(1 + .08)

(1 + .08)

75 x 1.08 = $81 (is the amount in her account after 1 year)

$81.00 - $75.00 = $6.00 (is the compound interest earned over 1 year)

Answer (d) is the correct answer

3.

Mitch has $700 in his checking account that is earning 12% interest, compounded annually. How much compound interest to the nearest rounded 100th will he earn in 1 year and what will be the new amount of his checking account?

Compound Interest Earned: $54.00; Amount in Savings: $754.00

Compound Interest Earned: $64.00; Amount in Savings: $764.00

Compound Interest Earned: $74.00; Amount in Savings: $774.00

Compound Interest Earned: $84.00; Amount in Savings: $784.00

The compound formula is A = P(1 + r)^{t}. Substituting the letters for numbers we get:

700(1 + .12)^{1}

(1 + .12)^{1} = (1.12)

700 x 1.12 = $784.00 (is the amount in savings after 1 year)

$784.00 - $700.00 = $84.00 (is the compound interest earned over 1 year)

__Solution__: Mitch will earn $84.00 in compound interest in 1 year and the full amount in his checking will be $784.00.

Answer (d) is the correct answer

700(1 + .12)

(1 + .12)

700 x 1.12 = $784.00 (is the amount in savings after 1 year)

$784.00 - $700.00 = $84.00 (is the compound interest earned over 1 year)

Answer (d) is the correct answer

4.

Penny deposited $280.00 into her savings account that is earning 5.6% interest, compounded annually. How much compound interest to the nearest rounded penny will she earn in 3 years and what will be the new amount of her savings?

Compound Interest Earned: $607.04; Amount in Savings: $887.04

Compound Interest Earned: $60.70; Amount in Savings: $340.70

Compound Interest Earned: $50.40; Amount in Savings: $330.40

Compound Interest Earned: $54.00; Amount in Savings: $334.00

The compound formula is A = P(1 + r)^{t}. Substituting the letters for numbers we get:

280(1 + .056)^{3}

(1 + .056)^{3} = (1.056 x 1.056 x 1.056) = 1.1775836 rounded to 1.18 (Remember that since the time number (i.e., 3 years here) is placed to the 3rd power [or cubed] we multiply the number by itself 3 times. We do not multiply 1.056 x 3.)

280 x 1.18 = $330.40 (is the amount in savings after 3 years)

$330.40 - $280.00 = $50.40 (is the compound interest earned over 3 years)

__Solution__: Penny will earn $50.40 in compound interest and her savings in 3 years will be $330.40.

Answer (c) is the correct answer

280(1 + .056)

(1 + .056)

280 x 1.18 = $330.40 (is the amount in savings after 3 years)

$330.40 - $280.00 = $50.40 (is the compound interest earned over 3 years)

Answer (c) is the correct answer

5.

Paul and Kristi bought a new boat for $154,000.00. The lender gave them a loan at 4.12% interest, compounded annually, for 10 years. How much compound interest will accrue over the 10 years and what will be the full amount that Paul and Kristi will have to pay back?

Compound Interest Accrued: $72,000.00; Full Amount to Pay-Off Loan: $226,000.00

Compound Interest Accrued: $77,000.00; Full Amount to Pay-Off Loan: $231,000.00

Compound Interest Accrued: $81,000.00; Full Amount to Pay-Off Loan: $393,000.00

Compound Interest Accrued: $83,000.00; Full Amount to Pay-Off Loan: $395,000.00

The compound formula is A = P(1 + r)^{t}. Substituting the letters for numbers we get:

154,000(1 + .0412)^{10}

(1 + .0412)^{10} = (1.0412 x 1.0412 x 1.0412 x 1.0412 x 1.0412 x 1.0412 x 1.0412 x 1.0412 x 1.0412 x 1.0412) = 1.4974127 rounded to 1.5

154,000 x 1.5 = $231,000.00 (is the full amount owed on the loan after 10 years)

$231,000.00 - $154,000.00 = $77,000.00 (is the compound interest accrued over 10 years)

__Solution__: Paul and Kristi’s loan accrued $77,000.00 in compound interest over the 10 years and the full amount that they will have to pay back is $231,000.00.

Answer (b) is the correct answer

154,000(1 + .0412)

(1 + .0412)

154,000 x 1.5 = $231,000.00 (is the full amount owed on the loan after 10 years)

$231,000.00 - $154,000.00 = $77,000.00 (is the compound interest accrued over 10 years)

Answer (b) is the correct answer

6.

Grandpa Jones has $90,000.00 in the bank which is earning 13% interest, compounded annually. If he does not touch this account, how much compound interest will he earn in 5 years and what will be the new amount of his bank account?

Compound Interest Earned: $72,600.00; Amount in Savings: $162,600.00

Compound Interest Earned: $73,600.00; Amount in Savings: $163,600.00

Compound Interest Earned: $74,600.00; Amount in Savings: $164,600.00

Compound Interest Earned: $75,600.00; Amount in Savings: $165,600.00

The compound formula is A = P(1 + r)^{t}. Substituting the letters for numbers we get:

90,000(1 + .13)^{5}

(1 + .13)^{5} = (1.13 x 1.13 x 1.13 x 1.13 x 1.13) = 1.8424351 rounded to 1.84

90,000 x 1.84 = $165,600 (is the amount in his account after 5 years)

$165,600.00 - $90,000.00 = $75,600.00 (is the compound interest earned over 5 years)

__Solution__: Grandpa will earn $75,600.00 in compound interest in 5 years and the full amount in his bank account will be $165,600.00.

Answer (d) is the correct answer

90,000(1 + .13)

(1 + .13)

90,000 x 1.84 = $165,600 (is the amount in his account after 5 years)

$165,600.00 - $90,000.00 = $75,600.00 (is the compound interest earned over 5 years)

Answer (d) is the correct answer

7.

Julie deposited $967.00 into her savings account that is earning 5.85% interest, compounded annually. How much compound interest to the nearest rounded 100th will she earn in 2 years and what will be the new amount of her savings?

Compound Interest Earned: $116.04; Amount in Savings: $1,083.04

Compound Interest Earned: $117.04; Amount in Savings: $1,084.04

Compound Interest Earned: $118.04; Amount in Savings: $1,085.04

Compound Interest Earned: $119.04; Amount in Savings: $1,086.04

The compound formula is A = P(1 + r)^{t}. Substituting the letters for numbers we get:

967(1 + .0585)^{2}

(1 + .0585)^{2} = (1.0585 x 1.0585) = 1.1204222 rounded to 1.12

967 x 1.12 = $1,083.04 (is the amount in savings after 2 years)

$1,083.04 - $967.00 = $116.04 (is the compound interest earned over 2 years)

__Solution__: Julie will earn $116.04 in compound interest in 2 years and her savings will be $1,083.04.

Answer (a) is the correct answer

967(1 + .0585)

(1 + .0585)

967 x 1.12 = $1,083.04 (is the amount in savings after 2 years)

$1,083.04 - $967.00 = $116.04 (is the compound interest earned over 2 years)

Answer (a) is the correct answer

8.

Phillip took out a small loan of $500.00 at an interest rate of 11%, compounded annually. He will pay the full amount back in 2 years. What will be the full amount of money Phillip will have to pay back and how much of that will be the compound interest?

Compound Interest Accrued: $115.00; Full Amount to Pay-Off Loan: $615.00

Compound Interest Accrued: $105.00; Full Amount to Pay-Off Loan: $605.00

Compound Interest Accrued: $135.00; Full Amount to Pay-Off Loan: $635.00

Compound Interest Accrued: $95.00; Full Amount to Pay-Off Loan: $595.00

The compound formula is A = P(1 + r)^{t}. Substituting the letters for numbers we get:

500(1 + .11)^{2}

(1 + .11)^{2} = (1.11 x 1.11) = 1.2321 rounded to 1.23

500 x 1.23 = $615.00 (is the full amount needed to pay off the loan after 2 years)

$615.00 - $500.00 = $115.00 (is the compound interest accrued over 2 years)

__Solution__: Phillip’s loan accrued $115.00 in compound interest over the 2 years and the full amount that he will have to pay back is $615.00.

Answer (a) is the correct answer

500(1 + .11)

(1 + .11)

500 x 1.23 = $615.00 (is the full amount needed to pay off the loan after 2 years)

$615.00 - $500.00 = $115.00 (is the compound interest accrued over 2 years)

Answer (a) is the correct answer

9.

The sports department of Ridgeville High School took out a 2 year loan in the amount of $28,000.00 to buy all new uniforms. The loan is earning 5.24% interest, compounded annually. How much compound interest to the nearest rounded 100th will accrue over 2 years and what will be the full amount that the sports department will have to pay back?

Compound Interest Accrued: $2,080.00; Full Amount to Pay-Off Loan: $30,080.00

Compound Interest Accrued: $3,080.00; Full Amount to Pay-Off Loan: $31,080.00

Compound Interest Accrued: $3,060.00; Full Amount to Pay-Off Loan: $31,060.00

Compound Interest Accrued: $3,180.00; Full Amount to Pay-Off Loan: $31,180.00

The compound formula is A = P(1 + r)^{t}. Substituting the letters for numbers we get:

28,000(1 + .0524)^{2}

(1 + .0524)^{2} = (1.0524 x 1.0524) = 1.1075457 rounded to 1.11

28,000 x 1.11 = $31,080.00 (is the full amount owed on the loan after 2 years)

$31,080.00 - $28,000.00 = $3,080.00 (is the compound interest accrued over 2 years)

__Solution__: The sports department’s loan accrued $3,080.00 in compound interest over the 2 years and the full amount that he will have to pay back is $31,080.00.

Answer (b) is the correct answer

28,000(1 + .0524)

(1 + .0524)

28,000 x 1.11 = $31,080.00 (is the full amount owed on the loan after 2 years)

$31,080.00 - $28,000.00 = $3,080.00 (is the compound interest accrued over 2 years)

Answer (b) is the correct answer

10.

Caleb has $2,900 in his savings account that is earning 6% interest, compounded annually. How much compound interest to the nearest rounded 100th will he earn (accrue) in 4 years and what will be the new amount of his savings account?

Compound Interest Accrued: $854.00; Full Amount in Savings: $3,754.00

Compound Interest Accrued: $804.00; Full Amount in Savings: $3,704.00

Compound Interest Accrued: $754.00; Full Amount in Savings: $3,654.00

Compound Interest Accrued: $704.00; Full Amount in Savings: $3,604.00

The compound formula is A = P(1 + r)^{t}. Substituting the letters for numbers we get:

2,900(1 + .06)^{4}

(1 + .06)^{4} = (1.06 x 1.06 x 1.06 x 1.06) = 1.2624769 rounded to 1.26

2,900 x 1.26 = $3,654.00 (is the full amount in the savings account after 4 years)

$3,654.00 - $2,900.00 = $754.00 (is the compound interest accrued over 4 years)

__Solution__: Caleb’s savings accrued $754.00 in compound interest over the 4 years and the full amount that he now has in his savings account is $3,654.00.

Answer (c) is the correct answer

2,900(1 + .06)

(1 + .06)

2,900 x 1.26 = $3,654.00 (is the full amount in the savings account after 4 years)

$3,654.00 - $2,900.00 = $754.00 (is the compound interest accrued over 4 years)

Answer (c) is the correct answer

^{t}. Substituting the letters for numbers we get:312,000(1 + .0375)

^{6}(1 + .0375)

^{6}= (1.0375 x 1.0375 x 1.0375 x 1.0375 x 1.0375 x 1.0375) = 1.2471783 rounded to 1.25312,000 x 1.25 = $390,000.00 (is the full amount owed on the loan after 6 years)

$390,000.00 - $312,000.00 = $78,000.00 (is the compound interest accrued over 6 years)

Solution: Farmer Richards’ loan accrued $78,000.00 in compound interest over the 6 years and the full amount that he will have to pay back is $390,000.00.Answer (c) is the correct answer