11. A promissory note is a commitment to pay a certain amount of money on a given date, called the date of maturity.
12. When a promissory note is cashed by a bank in advance of its date of maturity, the bank deducts a discount from the principal and pays the rest to the depositor.
13. To find the bank discount:
a. Find the time between the date the note is deposited and its date of maturity, and express this time as a fractional part of a year.
b. Rename the rate as a fraction.
c. Multiply the principal by the time and the rate to find the bank discount.
d. If required, subtract the bank discount from the original principal to find the amount the bank will pay the depositor.
Problem: A $400 note drawn up on August 12, 2004, for ninety days is deposited at a bank on September 17, 2004. The bank charges a 61
2% discount on notes. How much will the depositor receive?
SOLUTION: From August 12, 2004 to September 17, 2004, is thirty-six days.
This means that the note has fifty-four days to run.
54 days 5 54
360of a year 61
2% 513
2% 5 13 200
$400 3 13 2003 54
360539 10 5$3.90
$400 2 $3.90 5 $396.10 Answer: The depositor will receive $396.10
PRACTICE TEST
1. What is the simple interest on $460 for two years at 81
2. For borrowing $300 for one month, a man was charged $6. The rate of in-terest was
3. At a simple interest rate of 5% a year, the principal that will give $12.50 interest in six months is
(A) $250 two months and fifteen days.
(A) $ 9.50
6. The scholarship board of a certain college lent a student $200 at an an-nual rate of 6% from September 30 until December 15. To repay the loan and accumulated interest, the student must give the college an amount clos-est to which one of the following?
(A) $202.50 (B) $203.00 (C) $203.50 (D) $212.00
7. If $300 is invested at simple interest so as to yield a return of $18 in nine months, the amount of money that must be invested at the same rate of interest so as to yield a return of $120 in six months is
(A) $3,000 (B) $3,300 (C) $2,000 (D) $2,300
8. When the principal is $600, the dif-ference over the course of one year between simple interest at 12% per annum and interest compounded semiannually at 12% per annum is (A) $2.16
(B) $21.60 (C) $ .22 (D) $0.00
9. What is the compound interest on
$600, compounded quarterly, at 6%
for nine months?
(A) $27.38 (B) $27.40 (C) $27.41 (D) $27.42
10. A ninety-day note for $1,200 is signed on May 12. Seventy-five days later the note is deposited at a bank that charges 8% discount on notes.
The bank discount is (A) $8.40
(B) $2.60 (C) $2.00 (D) $4.00
ANSWERS AND EXPLANATIONS
1. The correct answer is (C).Principal 5 $460
2. The correct answer is (C).
Principal 5 $300
3. The correct answer is (B).
Rate 5 5% 5 .05 4. The correct answer is (B).
Time = 2 months 15 days 5 75 days or 75 5. The correct answer is (A).
Principal 5 $300
6. The correct answer is (A).
Principal 5 $200 Rate 5 .06 5 6
100
Time from Sept. 30 until Dec. 15 is 76 days. (31 days in October, 30 days in November, 15 days in December)
76 days 5 76 360year
1 Interest 5 $200 3 6
1003 76 360
1 60
5 $152
60 5$2.53
$200 1 $2.53 5 $202.53 2
The correct answer is (A), $202.50.
7. The correct answer is (A).
Principal 5 $300 Interest 5 $18
Time 5 9
12years 53 4year
$300 33
45$225
$18 4 225 5 .08 Rate is 8%
To yield $120 at 8% in 6 months:
Interest 5 $120 Rate 5 .08 Time 51
2year .08 31
25.04
$120 4 .04 5 $3,000 must be invested 8. The correct answer is (A).
Simple interest:
Principal 5 $600 Rate 5 .12 Time 5 1 year
Interest 5 $600 3 .12 3 1 5$72.00
Compound Interest:
Principal 5 $600 Period of compounding 51
2year Rate 5 .12
For the first period,
Interest 5 $600 3 .12 31 2 5$36
New principal 5 $600 1 $36 5$636 For the second period,
Interest 5 $636 3 .12 31 2 5$38.16
New principal 5 $636 1 $38.16 5$674.16 Total interest 5 $74.16
Difference 5 $74.16 2 $72.00 5$2.16
9. The correct answer is (C).
Principal 5 $600 Rate 5 6% 5 6
100 Time (period of compounding) 5 3
12year 51 4year
In 9 months, the interest will be computed 3 times.
For the first quarter, Interest 5 $600 3 6
10031 4 5$9
New principal at end of first quarter:
$600 1 $9 5 $609 For second quarter,
Interest 5 $609 3 6 10031
4 5 $3654
400 5$9.135, or $9.14 New principal at end of second quarter:
$609 1 $9.14 5 $618.14 For third quarter,
Interest 5 $618.14 3 6 10031
4 5 $3708.84
400 5$9.27
Total interest for the 3 quarters:
$9 1 $9.14 1 $9.27 5 $27.41
10. The correct answer is (D).
Principal 5 $1,200
Time 5 90 days 2 75 days 515 days
15 days 5 15 360year Rate 5 8% 5 8 100
1 Bank discount 5 $1,200 3 8
1003 15 360
1 45
5 $180 45 5$4 12
TAXATION
1. The following facts should be taken into consideration when solving taxation problems:
a. Taxes may be expressed as a percent or in terms of money based on a certain denomination.
b. A surtax is an additional tax besides the regular tax rate in percent.
2. In taxation, there are usually three items involved: the amount taxable, which is called the base, the tax rate, and the tax itself.
3. To find the tax when given the base and the tax rate in percent:
a. Rename the tax rate as a decimal.
b. Multiply the base by the tax rate.
Problem: How much would be realized on $4,000 if taxed at 15%?
SOLUTION: 15% 5 .15
$4,000 3 .15 5 $600 Answer: Tax 5 $600
4. To find the tax rate in percent form when given the base and the tax:
a. Divide the tax by the base.
b. Rename as a percent.
Problem: Find the tax rate at which $5,600 would yield $784.
SOLUTION: $784 4 $5,600 5 .14 .14 5 14%
Answer: Tax rate 5 14%
5. To find the base when given the tax rate and the tax:
a. Rename the tax rate as a decimal.
b. Divide the tax by the tax rate.
Problem: What amount of money taxed 3% would yield $75?
SOLUTION: 3% 5 .03
$75 4 .03 5 $2,500
6. When the tax rate is fixed and expressed in terms of money, take into consideration the denomination upon which it is based; that is, consider whether it is based on every $100, or $1,000, etc.
7. To find the tax when given the base and tax rate in terms of money:
a. Divide the base by the denomination upon which the tax rate is based.
b. Multiply this quotient by the tax rate.
Problem: If the tax rate is $3.60 per $1,000, find the tax on $470,500.
SOLUTION: $475,500 4 $1,000 5 470.5 470.5 3 $3.60 5 $1,693.80 Answer: $1,693.80
8. To find the tax rate based on a certain denomination when given the base and the tax derived:
a. Divide the base by the denomination indicated.
b. Divide the tax by this quotient.
Problem: Find the tax rate per $100 that would be required to raise
$350,000 on $2,000,000 of taxable property.
SOLUTION: $2,000,000 4 $100 5 $20,000
$350,000 4 20,000 5 $17.50 Answer: Tax rate 5 $17.50 per $100
9. Since a surtax is an additional tax besides the regular tax, to find the total tax:
a. Rename the regular tax rate as a decimal.
b. Multiply the base by the regular tax rate.
c. Rename the surtax rate as a decimal.
d. Multiply the base by the surtax rate.
e. Add both taxes.
Problem: Assuming that the tax rate is 21
3% on liquors costing up to $3, and 3% on those costing from $3 to $6, and 31
2% on those from
$6 to $10, what would be that tax on a bottle costing $8 if there is a surtax of 5% on all liquors above $5?
SOLUTION: An $8 bottle falls within the category of $6 to $10. The tax rate on such a bottle is
31
2% 5 .035
$8.00 3 .035 5 $.28 surtax rate 5 5% 5 .05
$8.00 3 .05 5 $.40
$.28 1 $.40 5 $.68 Answer: Total tax 5 $.68
PRACTICE TEST
1. Mr. Jones’ income for a year is
$15,000. He pays $2,250 for income taxes. The percent of his income that he pays for income taxes is
(A) 9% to be raised is $64.40, what is the base? base of $338,500 would yield
$616.07?
(A) $1.08 (B) $1.90 (C) $1.95 (D) $1.82
4. A man buys an electric light bulb for 54¢, which includes a 20% tax. What is the cost of the bulb without the tax?
6. A piece of property is assessed at
$22,850 and the tax rate is $4.80 per
$1,000 of assessed valuation. What is the amount of tax that must be paid on the property?
(A) $109 (B) $112 (C) $109.68 (D) $112.68
7. $30,000 of land is assessed at 120%
of its value. If the tax rate is $5.12 per $1,000 assessed valuation, the amount of tax to be paid is
(A) $180.29 (B) $184.32 (C) $190.10 (D) $192.29
8. Of the following real estate tax rates, which is the greatest?
(A) $31.25 per $1,000 (B) $3.45 per $100 (C) 32¢ per $10 (D) 3¢ per $1
9. A certain community needs
$185,090.62 to cover its expenses. If its tax rate is $1.43 per $100 of as-sessed valuation, what must be the assessed value of its property?
(A) $12,900,005 (B) $12,943,400 (C) $12,940,000 (D) $12,840,535
10. A man’s taxable income is $14,280.
The state tax instructions tell him to pay 2% on the first $3,000 of his taxable income, 3% on each of the second and third $3,000, and 4% on the remainder. What is the total amount of income tax that he must pay?
(A) $265.40 (B) $309.32 (C) $451.20 (D) $454.62
ANSWERS AND EXPLANATIONS
1. C 2. B
3. D 4. C
5. C 6. C
7. B 8. B
9. B 10. C
1. The correct answer is (C).
Tax 5 $2,250 Base 5 $15,000 Tax Rate 5 Tax 4 Base
Tax Rate 5 $2,250 4 $15,000 5 .15 Tax rate 5 .15 5 15%
2. The correct answer is (B).
Tax Rate 5 31
2% 5 .035 Tax 5 $64.40
Base 5 Tax 4 Tax rate Base 5 $64.40 4 .035
5$1,840 3. The correct answer is (D).
Base 5 $338,500 Tax 5 $616.07 Denomination 5 $1,000
$338,500 4 $1,000 5 338.50
$616.07 4 338.50 5 $1.82 per $1,000
4. The correct answer is (C). 54¢ is 120% of the base (cost without tax).
Base 5 54 4 120%
554 4 1.20 545¢
5. The correct answer is (C).
Base 5 $3,650 Tax 5 $164.25 Tax rate 5 Tax 4 Base
5$164.25 4 $3,650 5.045
5 41 2% 6. The correct answer is (C).
Base 5 $22,850 Denomination 5 $1,000
Tax rate 5 $4.80 per thousand
$22,850
$1,000 522.85 22.85 3 $4.80 5 $109.68
7. The correct answer is (B).
Base 5 Assessed valuation 5 120% of $30,000 51.20 3 $30,000 5$36,000 Denomination 5 $1,000
Tax rate 5 $5.12 per thousand
$36,000
$1,000 536 36 3 $5.12 5 $184.32
8. The correct answer is (B). Express each tax rate as a decimal:
$31.25 per $1,000 531.25
1,0005.03125
$3.45 per $100 53.45
100 5.0345 32¢ per $10 5.32
105.0320 3¢ per $1 5.03
1 5.0300 The greatest decimal is .0345
So the correct answer is (B), $3.45 per $1,000.
9. The correct answer is (B).
Tax rate 5 $1.43 per $100 51.43
100 5.0143 51.43%
Tax 5 $185,090.62 Base 5 Tax 4 Rate
5185,090.62 4 .0143 5$12,943,400 10. The correct answer is (C).
First $3,000: .02 3 $3,000 5 $60.00 Second $3,000: .03 3 $3,000 5 $90.00 Third $3,000: .03 3 $3,000 5 $90.00 Remainder ~$14,280 2 $9,000!: .04 3 $5,280 5 $211.20 Total Tax 5 $451.20