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Tyler has $14.79 in his sock bank.
Consumer Math (Calculating Compound Interest to the Penny)
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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.
1.
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
2.
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
3.
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
4.
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
5.
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
6.
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
7.
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
8.
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
9.
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
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
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
10.
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
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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