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.
It costs only $12.50 per month to play this quiz and over 3,500 others that help you with your school work. You can subscribe on the page at Join Us
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.
[readmore]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.
[/readmore]
|
|
||||||||||||||||||||||||
|
|
||||||||||||||||||||||||
|
|
||||||||||||||||||||||||
|
|
||||||||||||||||||||||||
|
|
|
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 |
||||||||||||||||||||||||
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 |
The compound formula is A = P(1 + r)t. Substituting the letters for numbers we get:
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 |
||||||||||||||||||||||||
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 |
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 |
||||||||||||||||||||||||
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 |
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 |
||||||||||||||||||||||||
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 |
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 |
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