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Tyler has $14.79 in his sock bank.
Consumer Math (Calculating Compound Interest to the Penny)
This Math quiz is called 'Consumer Math (Calculating Compound Interest to the Penny)' and it has been written by teachers to help you if you are studying the subject at middle school. Playing educational quizzes is a fabulous way to learn if you are in the 6th, 7th or 8th grade - aged 11 to 14.
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As you may recall, 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.
In a separate quiz, you would calculate the compound interest to the whole dollar, meaning when you had to multiply the interest by its power, you were to round that amount to the nearest 100th. In this quiz, you will be required to calculate the interest by the full string of its power or to the penny. [NOTE: You will need to use a calculator to do the problems here.] This will enable you to more accurately determine the amount of interest and the full amount to be paid back or that will be left in savings at the end of the term.
So to just quickly refresh you on what “interest” is in the monetary world of saving and borrowing, it is the amount of extra money you earn or you have to pay back.
As we will be only dealing with compound interest calculations in this quiz, the formula that will be used 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)
Okay, let’s work out one problem together.
You have to borrow $850.00 at an interest rate of 3.28% for 2 years. Using the compound interest formula that will read as follows:
A = 850(1 + .0328)2
850(1.0328)2
(1.0328 x 1.0328) = 1.0666758 (You need to use this entire percentage string to do the problem.)
850 x 1.0666758 = 906.67443 (Round this number to the nearest penny making it $906.67.)
$906.67 - $850.00 = $56.67
$56.67 is the compound interest over two years and
A = $906.67 is the full amount that will have to be paid back over the two years.
Had you rounded the percentage off to 1.07, the full amount to pay off would have come to $909.50. It is an approximate amount but not the “exact” amount. When figuring out compound interest to the exact amount, you must use the percentage string.
1.
Brett has $11,500 in his savings account that is earning 6.5% interest, compounded annually. How much compound interest will he earn in 5 years and what will be the new amount of his savings account?
Compound Interest Accrued: $4,256.00; Full Amount in Savings: $15,756.00
Compound Interest Accrued: $4,056.00; Full Amount in Savings: $15,556.00
Compound Interest Accrued: $3,856.00; Full Amount in Savings: $15,356.00
Compound Interest Accrued: $3,556.00; Full Amount in Savings: $15,056.00
2.
Billy’s parents opened up a savings account for him when he was born. They put $2,000.00 into the account where it has been earning 6% interest, compounded annually, for 12 years. How much compound interest has the account earned/accrued and what amount should be in the account now?
Compound Interest Earned: $2,324.39; Amount in Savings: $4,324.39
Compound Interest Earned: $2,224.39; Amount in Savings: $4,224.39
Compound Interest Earned: $2,124.39; Amount in Savings: $4,124.39
Compound Interest Earned: $2,024.39; Amount in Savings: $4,024.39
The compound formula is A = P(1 + r)t. Substituting the letters for numbers we get:
2,000(1 + .06)12
(1 + .06)12 = (1.06 x 1.06 x 1.06 x 1.06 x 1.06 x 1.06 x 1.06 x 1.06 x 1.06 x 1.06 x 1.06 x 1.06) = 2.012196
2,000 x 2.012196 = $4,024.392 (Rounded to the nearest penny it is $4,024.39 and it is the amount in the savings account after 12 years)
$4,024.39 - $2,000.00 = $2,024.39 (is the compound interest earned over 12 years)
Solution: Billy’s savings account has earned $2,024.39 in compound interest in 12 years and the full amount in the account should now be $4,024.39.
Answer (d) is the correct answer
2,000(1 + .06)12
(1 + .06)12 = (1.06 x 1.06 x 1.06 x 1.06 x 1.06 x 1.06 x 1.06 x 1.06 x 1.06 x 1.06 x 1.06 x 1.06) = 2.012196
2,000 x 2.012196 = $4,024.392 (Rounded to the nearest penny it is $4,024.39 and it is the amount in the savings account after 12 years)
$4,024.39 - $2,000.00 = $2,024.39 (is the compound interest earned over 12 years)
Solution: Billy’s savings account has earned $2,024.39 in compound interest in 12 years and the full amount in the account should now be $4,024.39.
Answer (d) is the correct answer
3.
Mabel has a retirement account with $49,000.00. It is earning 4.32% interest, compounded annually. If she doesn’t touch her account for 7 years, how much compound interest will it earn and what will be the new balance of her retirement account?
Compound Interest Earned: $15,882.34; Amount in Savings: $64,882.34
Compound Interest Earned: $14,882.34; Amount in Savings: $63,882.34
Compound Interest Earned: $16,882.34; Amount in Savings: $65,882.34
Compound Interest Earned: $18,882.34; Amount in Savings: $67,882.34
The compound formula is A = P(1 + r)t. Substituting the letters for numbers we get:
49,000(1 + .0432)7
(1 + .0432)7 = (1.0432 x 1.0432 x 1.0432 x 1.0432 x 1.0432 x 1.0432 x 1.0432) = 1.3445375
49,000 x 1.3445375 = $65,882.337 (Rounded to the nearest penny it is $65,882.34 and it is the amount in the retirement account after 7 years)
$65,882.34 - $49,000.00 = $16,882.34 (is the compound interest earned over 7 years)
Solution: Mabel’s retirement account will earn $16,882.34 in compound interest in 7 years and the full amount in the retirement account will be $65,882.34.
Answer (c) is the correct answer
49,000(1 + .0432)7
(1 + .0432)7 = (1.0432 x 1.0432 x 1.0432 x 1.0432 x 1.0432 x 1.0432 x 1.0432) = 1.3445375
49,000 x 1.3445375 = $65,882.337 (Rounded to the nearest penny it is $65,882.34 and it is the amount in the retirement account after 7 years)
$65,882.34 - $49,000.00 = $16,882.34 (is the compound interest earned over 7 years)
Solution: Mabel’s retirement account will earn $16,882.34 in compound interest in 7 years and the full amount in the retirement account will be $65,882.34.
Answer (c) is the correct answer
4.
Jamison deposited $645.00 into a savings account that is earning 3.9% interest, compounded annually. How much compound interest to the nearest rounded penny will he earn in 2 years and what will be the new amount of his savings?
Compound Interest Earned: $50.29; Amount in Savings: $695.29
Compound Interest Earned: $51.29; Amount in Savings: $696.29
Compound Interest Earned: $52.29; Amount in Savings: $697.29
Compound Interest Earned: $53.29; Amount in Savings: $698.29
The compound formula is A = P(1 + r)t. Substituting the letters for numbers we get:
645(1 + .039)2
(1 + .039)2 = (1.039 x 1.039) = 1.079521
645 x 1.079521 = $696.29104 (Round this number to the nearest penny so you will have $696.29 as the amount in savings after 2 years)
$696.29 - $645.00 = $51.29 (is the compound interest earned over 2 years)
Solution: Jamison will earn $51.29 in compound interest and his savings in 2 years will be $696.29.
Answer (b) is the correct answer
645(1 + .039)2
(1 + .039)2 = (1.039 x 1.039) = 1.079521
645 x 1.079521 = $696.29104 (Round this number to the nearest penny so you will have $696.29 as the amount in savings after 2 years)
$696.29 - $645.00 = $51.29 (is the compound interest earned over 2 years)
Solution: Jamison will earn $51.29 in compound interest and his savings in 2 years will be $696.29.
Answer (b) is the correct answer
5.
The newly engaged couple took out a loan to pay for their wedding and honeymoon. They borrowed $15,000.00 at 3% and will pay it back in 2 years. How much compound interest will accrue over 2 years and what will be the full amount that the couple will have to pay back?
Compound Interest Accrued: $913.50; Full Amount to Pay-Off Loan: $15,913.50
Compound Interest Accrued: $943.50; Full Amount to Pay-Off Loan: $15,943.50
Compound Interest Accrued: $983.50; Full Amount to Pay-Off Loan: $15,983.50
Compound Interest Accrued: $993.50; Full Amount to Pay-Off Loan: $15,993.50
The compound formula is A = P(1 + r)t. Substituting the letters for numbers we get:
15,000(1 + .03)2
(1 + .03)2 = (1.03 x 1.03) = 1.0609
15,000 x 1.0609 = $15,913.50 (is the full amount owed on the loan after 2 years)
$15,913.50 - $15,000.00 = $913.50 (is the compound interest accrued over 2 years)
Solution: The couple’s loan accrued $913.50 in compound interest over the 2 years and the full amount that they will have to pay back is $15,913.50.
Answer (a) is the correct answer
15,000(1 + .03)2
(1 + .03)2 = (1.03 x 1.03) = 1.0609
15,000 x 1.0609 = $15,913.50 (is the full amount owed on the loan after 2 years)
$15,913.50 - $15,000.00 = $913.50 (is the compound interest accrued over 2 years)
Solution: The couple’s loan accrued $913.50 in compound interest over the 2 years and the full amount that they will have to pay back is $15,913.50.
Answer (a) is the correct answer
6.
Zachery took out a personal loan of $4,000.00 at an interest rate of 9%, compounded annually. He will pay the full amount back in 3 years. What will be the full amount of money Zachery will have to pay back and how much of that will be the compound interest?
Compound Interest Accrued: $1,080.12; Full Amount to Pay-Off Loan: $5,080.12
Compound Interest Accrued: $1,008.12; Full Amount to Pay-Off Loan: $5,008.12
Compound Interest Accrued: $1,180.12; Full Amount to Pay-Off Loan: $5,180.12
Compound Interest Accrued: $1,260.12; Full Amount to Pay-Off Loan: $5,260.12
The compound formula is A = P(1 + r)t. Substituting the letters for numbers we get:
4,000(1 + .09)3
(1 + .09)3 = (1.09 x 1.09 x 1.09) = 1.295029
4,000 x 1.295029 = $5,180.116 (Rounded to the nearest penny so $5,180.12 is the full amount needed to pay off the loan after 3 years)
$5,180.12 - $4,000.00 = $1,180.12 (is the compound interest accrued over 3 years)
Solution: Zachery’s loan accrued $1,180.12 in compound interest over the 3 years and the full amount that he will have to pay back is $5,180.12.
Answer (c) is the correct answer
4,000(1 + .09)3
(1 + .09)3 = (1.09 x 1.09 x 1.09) = 1.295029
4,000 x 1.295029 = $5,180.116 (Rounded to the nearest penny so $5,180.12 is the full amount needed to pay off the loan after 3 years)
$5,180.12 - $4,000.00 = $1,180.12 (is the compound interest accrued over 3 years)
Solution: Zachery’s loan accrued $1,180.12 in compound interest over the 3 years and the full amount that he will have to pay back is $5,180.12.
Answer (c) is the correct answer
7.
The public aquatic center took out a 4 year loan in the amount of $50,000.00 to buy all equipment. The loan is earning 2.97% interest, compounded annually. How much compound interest will accrue over 4 years and what will be the full amount that the public aquatic center will have to pay back?
Compound Interest Accrued: $5,909.90; Full Amount to Pay-Off Loan: $55,909.90
Compound Interest Accrued: $6,009.90; Full Amount to Pay-Off Loan: $56,009.90
Compound Interest Accrued: $6,109.90; Full Amount to Pay-Off Loan: $56,109.90
Compound Interest Accrued: $6,209.90; Full Amount to Pay-Off Loan: $56,209.90
The compound formula is A = P(1 + r)t. Substituting the letters for numbers we get:
50,000(1 + .0297)4
(1 + .0297)4 = (1.0297 x 1.0297 x 1.0297 x 1.0297) = 1.1241979
50,000 x 1.1241979 = $56,209.895 (Rounded to the nearest penny so $56,209.90 is the full amount owed on the loan after 4 years)
$56,209.90 - $50,000.00 = $6,209.90 (is the compound interest accrued over 4 years)
Solution: The public aquatic center’s loan accrued $6,209.90 in compound interest over the 4 years and the full amount that it will have to pay back is $56,209.90.
Answer (d) is the correct answer
50,000(1 + .0297)4
(1 + .0297)4 = (1.0297 x 1.0297 x 1.0297 x 1.0297) = 1.1241979
50,000 x 1.1241979 = $56,209.895 (Rounded to the nearest penny so $56,209.90 is the full amount owed on the loan after 4 years)
$56,209.90 - $50,000.00 = $6,209.90 (is the compound interest accrued over 4 years)
Solution: The public aquatic center’s loan accrued $6,209.90 in compound interest over the 4 years and the full amount that it will have to pay back is $56,209.90.
Answer (d) is the correct answer
8.
Tyler has $14.79 in his sock bank. His parents will pay him 50% interest, compounded, if he doesn’t touch the sock for 1 month. How much compound interest will accrue over 1 month and what will be the full amount that Tyler will get for not touching the money in his sock?
Compound Interest Earned: $7.38; Amount in Savings: $22.17
Compound Interest Earned: $7.39; Amount in Savings: $22.18
Compound Interest Earned: $7.40; Amount in Savings: $22.19
Compound Interest Earned: $7.41; Amount in Savings: $22.20
The compound formula is A = P(1 + r)t. Substituting the letters for numbers we get:
14.79(1 + .5)1
(1 + .5)1 = (1.5)
14.79 x 1.5 = $22.185 (Rounded to the nearest penny makes it $22.19 and this is the full amount Tyler will get after 1 month)
$22.19 - $14.79 = $7.40 (is the compound interest accrued over 1 month)
Solution: Tyler will have earned $7.40 in compound interest over the 1 month and the full amount that he will have in his sock will be $22.19.
Answer (c) is the correct answer
14.79(1 + .5)1
(1 + .5)1 = (1.5)
14.79 x 1.5 = $22.185 (Rounded to the nearest penny makes it $22.19 and this is the full amount Tyler will get after 1 month)
$22.19 - $14.79 = $7.40 (is the compound interest accrued over 1 month)
Solution: Tyler will have earned $7.40 in compound interest over the 1 month and the full amount that he will have in his sock will be $22.19.
Answer (c) is the correct answer
9.
Travis opened up a Christmas savings account and put in $1,500.00. The account will earn 16.4% interest, compounded annually. How much compound interest to the nearest rounded penny will he earn in 1 year and what will be the new amount of his Christmas savings account?
Compound Interest Earned: $546.00; Amount in Savings: $2,046.00
Compound Interest Earned: $446.00; Amount in Savings: $1,946.00
Compound Interest Earned: $344.00; Amount in Savings: $1,846.00
Compound Interest Earned: $246.00; Amount in Savings: $1,746.00
The compound formula is A = P(1 + r)t. Substituting the letters for numbers we get:
1,500(1 + .164)1
(1 + .164)1 = (1.164)
1,500 x 1.164 = $1,746.00 (is the amount in savings after 1 year)
$1,746.00 - $1,500.00 = $246.00 (is the compound interest earned over 1 year)
Solution: Travis will earn $246.00 in compound interest in 1 year and the full amount in his Christmas savings account will be $1,746.00.
Answer (d) is the correct answer
1,500(1 + .164)1
(1 + .164)1 = (1.164)
1,500 x 1.164 = $1,746.00 (is the amount in savings after 1 year)
$1,746.00 - $1,500.00 = $246.00 (is the compound interest earned over 1 year)
Solution: Travis will earn $246.00 in compound interest in 1 year and the full amount in his Christmas savings account will be $1,746.00.
Answer (d) is the correct answer
10.
The Fuller Law Firm has $2,600,000.00 in the bank which is earning 8.75% interest, compounded annually. If the firm does not touch this account, how much compound interest will it earn in 3 years and what will be the new amount of this bank account?
Compound Interest Earned: $763,960.30; Amount in Savings: $3,363,960.30
Compound Interest Earned: $743,960.30; Amount in Savings: $3,343,960.30
Compound Interest Earned: $703,960.30; Amount in Savings: $3,303,960.30
Compound Interest Earned: $963,960.30; Amount in Savings: $3,563,960.30
The compound formula is A = P(1 + r)t. Substituting the letters for numbers we get:
2,600,000(1 + .0875)3
(1 + .0875)3 = (1.0875 x 1.0875 x 1.0875) = 1.2861386
2,600,000 x 1.2861386 = $3,343,960.30 (is the amount in this account after 3 years)
$3,343,960.30 - $2,600,000.00 = $743,960.30 (is the compound interest earned over 3 years)
Solution: The Fuller Law Firm will earn $743,960.30 in compound interest in 3 years and the full amount in its bank account will be $3,343,960.30.
Answer (b) is the correct answer
2,600,000(1 + .0875)3
(1 + .0875)3 = (1.0875 x 1.0875 x 1.0875) = 1.2861386
2,600,000 x 1.2861386 = $3,343,960.30 (is the amount in this account after 3 years)
$3,343,960.30 - $2,600,000.00 = $743,960.30 (is the compound interest earned over 3 years)
Solution: The Fuller Law Firm will earn $743,960.30 in compound interest in 3 years and the full amount in its bank account will be $3,343,960.30.
Answer (b) is the correct answer
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11,500(1 + .065)5
(1 + .065)5 = (1.065 x 1.065 x 1.065 x 1.065 x 1.065) = 1.3700866
11,500 x 1.3700866 = $15,755.995 (Rounded to the nearest penny so $15,756.00 is the full amount in the savings account after 5 years)
$15,756.00 - $11,500.00 = $4,256.00 (is the compound interest accrued over 5 years)
Solution: Brett’s savings account accrued $4,256.00 in compound interest over the 5 years and the full amount that he now has in savings is $15,756.00.
Answer (a) is the correct answer