How to express the present value, final value coefficient, (formula), (what do P / A, P / F mean), calculation formula, how to calculate

How to express the present value, final value coefficient, (formula), (what do P / A, P / F mean), calculation formula, how to calculate

The calculation of the final value of compound interest f = P (1 + I) ^ n (1 + I) ^ n is the coefficient of final value of compound interest, expressed by (F / P, I, n) (^ is the power)
Calculation of the present value of compound interest P = f (1 + I) ^ (- n) (1 + I) ^ (- n) is the coefficient of present value of compound interest, expressed by (P / F, I, n)
(P / A, I, n) is the annuity present value coefficient

How to express the present value, final value coefficient, (formula), (P / A, calculation formula, how to calculate, specific point

There are two kinds of present value coefficient: A. annuity present value coefficient: (P / A, I, n) = (1 - (1 + I) negative n power) / I; B. compound interest present value coefficient: (P / F, I, n)) = (1 + I) negative n power
There are also two kinds of terminal value coefficient: A. annuity terminal value coefficient: (F / A, I, n) = ((1 + I) n power-1) / I; B. compound interest terminal value coefficient: (F / P, I, n) = (1 + I) n power. Where I is interest rate
In general, the present value and final value coefficients are given, but they are expressed as (P / A, I, n), (F / A, I, n), so you only need to remember the meaning of these formula symbols

How to understand the final value formula of ordinary annuity F=A+A(1+i)+A(1+i)2+A(1+i)3+.+A(1+i)n-1 Compound interest calculation That is, at the end of each year, the amount of a received and paid at the end of each year. What is the amount after n years? A at the end of the first year At the end of the second year, a × I (interest generated by a in the first year) + a (received and paid at the end of this year) = a (1 + I) At the end of the third year I understand both the first year and the second year, but I don't understand from the beginning of the third year. Why isn't the sum of the money received and paid in the first year and the second year as the principal at the end of the third year? Shouldn't it be (a + a (1 + I)) * (1 + I)?

The annuity received from year 1 to year 2 (a + I) is the annuity received from year 1 to year 2

What is the final value formula?

Second, the final value of compound interest, also known as the future value or the sum of principal and interest, refers to the value of a certain amount of funds at a certain point in the future

All mathematical formulas for Grades 1-6

The mathematical formula of grade 1-6 in primary school: number of each piece × number of copies = total number of copies △ number of copies = total number of copies ＋ number of copies = number of copies per copy 2,1 times × multiple = several times of times ＋ 1 times = Times several times ＋ 1 times = 1 times 3, speed × time = distance ＋ speed = time distance ＋ time = speed

All mathematical formulas for grades one to six in primary school

1. The circumference of a rectangle = (length + width) × 2 C = (a + b) × 2
2. Circumference of square = side length × 4, C = 4A
3. Area of rectangle = length × width s = ab
4. Area of square = side length × side length s = A.A = a
5. Area of triangle = bottom × height △ 2 s = ah △ 2
6. Area of parallelogram = base × height s = ah
7. Trapezoid area = (upper bottom + bottom) × height △ 2 s = (a + b) H △ 2
8. Diameter = radius × 2 D = 2R radius = diameter △ 2 r = D △ 2
9. Circumference of a circle = circumference × diameter = circumference × radius × 2 C = π d = 2 π R
10. Area of a circle = circumference × radius × radius? = π R
11. The surface area of cuboid = (length × width + length × height + width × height) × 2
12. Volume of cuboid = length × width × height v = ABH
13. The surface area of cube = edge length × edge length × 6 s = 6A
14. Volume of cube = edge length × edge length × edge length v = a.a.a = a
15. Side area of cylinder = perimeter of bottom circle × height s = Ch
16. The surface area of the cylinder = upper and lower bottom surface area + side area
S=2πr +2πrh=2π(d÷2) +2π(d÷2)h=2π(C÷2÷π) +Ch
17. Volume of cylinder = bottom area × height v = sh
V=πr h=π(d÷2) h=π(C÷2÷π) h
18. Volume of cone = base area × height △ 3
V=Sh÷3=πr h÷3=π(d÷2) h÷3=π(C÷2÷π) h÷3
1. Number of copies × number of copies = total number of copies / number of copies = total number of copies / number of copies = number of copies
2. 1 times × multiple = several times several times △ 1 times = multiple several times × = 1 times
3. Speed × time = distance / distance / speed = time / distance / time = speed
4. Unit price × quantity = total price / unit price = total quantity / total price / quantity = unit price
5. Work efficiency × working time = total work, total amount of work, work efficiency = working time, total amount of work, working time = work efficiency
6. Addend + addend = and - one addend = another
7. Subtraction minus = subtraction subtraction = subtraction difference + subtraction = subtraction
8. Factor × factor = product product △ one factor = another factor
9. Divisor △ divisor = quotient divisor △ quotient = divisor quotient × divisor = divisor
Primary school mathematics figure calculation formula
1. Square C perimeter s area a side length perimeter = side length × 4 C = 4A area = side length × side length s = a × a
2. Cube V: Volume A: edge length surface area = edge length × edge length × 6 s surface = a × a × 6 volume = edge length × edge length × edge length v = a × a × a
3. Rectangle
C perimeter s area a side length
Perimeter = (length + width) × 2
C=2(a+b)
Area = length × width
S=ab
4. Cuboid
5: Volume s: Area A: length B: width H: height
(1) Surface area (L × W + L × H + W × h) × 2
S=2(ab+ah+bh)
(2) Volume = length × width × height
V=abh
5 triangle
S area a bottom h height
Area = bottom × height △ 2
s=ah÷2
Triangle height = area × 2 △ bottom
Triangle base = area × 2 △ height
6 parallelogram
S area a bottom h height
Area = bottom × height
s=ah
7 trapezoid
S area a upper bottom B bottom h height
Area = (bottom + bottom) × height △ 2
s=(a+b)× h÷2
8 round
S area C circumference Π d = diameter r = radius
(1) Circumference = diameter ×Π = 2 ×Π × radius
C=∏d=2∏r
(2) Area = radius x radius x Π
9 cylinder
v: Volume H: height s; bottom area R: bottom radius C: bottom perimeter
(1) Side area = perimeter of bottom surface × height
(2) Surface area = side area + bottom area × 2
(3) Volume = bottom area × height
(4) Volume = side area △ 2 × radius
Cone 10
v: Volume H: height s; bottom area R: bottom radius
Volume = bottom area × height △ 3
Total number of copies = average
Sum difference problem
(sum + difference) △ 2 = large number
(sum difference) 2 = decimal
The problem of sum times
And △ (multiple-1) = decimal
Decimal × multiple = large number
(or sum decimal = large number)
Differential multiple problem
Difference × (multiple-1) = decimal
Decimal × multiple = large number
(or decimal + difference = large number)
Tree planting
1. Tree planting on non closed lines can be divided into the following three situations:
(1) if trees are to be planted at both ends of an unclosed line, then:
Number of plants = number of segments + 1 = total length △ plant spacing-1
Total length = plant spacing × (number of plants - 1)
Spacing = 1
(2) if trees are to be planted at one end of an unclosed line and not at the other end, then:
The number of plants is equal to the number of plants
Total length = spacing × number of trees
Plant spacing = total length △ number of trees
(3) if trees are not planted at both ends of the unclosed line, then:
Number of plants = number of segments-1 = total length × plant spacing-1
Total length = plant spacing × (number of plants + 1)
Plant spacing = total length × (number of plants + 1)
2. The quantitative relationship of tree planting on closed lines is as follows
Number of plants = number of segments = total length × plant spacing
Total length = spacing × number of trees
Plant spacing = total length △ number of trees
Profit and loss
(profit + loss) × the difference between the two distributions = the number of shares participating in the distribution
(large profit small profit) × the difference between the two distributions = the number of shares participating in the distribution
(large deficit small deficit) × the difference between the two distributions = the number of shares participating in the distribution
Encounter problem
Encounter distance = speed and X encounter time
Encounter time = encounter distance △ speed sum
Speed sum = encounter distance △ encounter time
Follow up on Problems
Chase distance = speed difference × pursuit time
Catching time = chasing distance △ speed difference
Speed difference = pursuit distance ×pursuit time
Flow problems
Downstream velocity = still water velocity + current velocity
Countercurrent velocity = still water velocity current velocity
Still water velocity = (downstream velocity + countercurrent velocity) × 2
Flow velocity = (downstream velocity - countercurrent velocity) × 2
Concentration problem
Weight of solute + weight of solvent = weight of solution
Weight of solute × weight of solution × 100% = concentration
Weight of solution × concentration = weight of solute
Weight of solute △ concentration = weight of solution
Profit and discount
Profit = selling price - cost
Profit rate = profit ＋ cost × 100% = (selling price ＋ cost-1) × 100%
Up / down amount = principal × up / down percentage
Discount = actual price × original price × 100% (discount < 1)
Interest = principal × interest rate × time
After tax interest = principal × interest rate × time × (1-20%)
time conversion
1 century = 100 years, 1 year = December
The big months (31 days) are: January, March, may, July, August, October and December
Small months (30 days): April, June, September and November
February 28 in normal year and February 29 in leap year
There are 365 days in a normal year and 366 days in a leap year
1 day = 24 hours, 1 hour = 60 minutes
1 minute = 60 seconds 1 hour = 3600 seconds product = base area × high V = sh
Part one: Concept
1. Additive commutative law: two numbers add to exchange the position of the adder, and the sum remains unchanged
2. Law of combination of addition: when three numbers are added, the first two numbers are added, or the last two numbers are added first, and then the third number is added, and the sum remains unchanged
3. Commutative law of multiplication: when two numbers are multiplied, the position and product of exchange factor remain unchanged
4. The law of combination of multiplication: when three numbers are multiplied, the first two numbers are multiplied, or the last two numbers are multiplied first, and then the third number is multiplied, and their product remains unchanged
5. The distributive law of multiplication: when the sum of two numbers is multiplied by the same number, two addends can be multiplied with this number respectively, and then the two products can be added together. For example: (2 + 4) × 5 = 2 × 5 + 4 × 5
6. The nature of division: in division, the divisor and the divisor expand (or shrink) the same multiple at the same time, and the quotient remains unchanged. O is divided by any number that is not o and gets o
Simple multiplication: multiplication with o at the end of the multiplicand and can be multiplied first. Zero does not participate in the operation. Several zeros are dropped and added to the end of the product
7. What is an equation? An equation in which the number on the left of the equal sign is equal to the value on the right of the equal sign is called an equation. The basic property of the equation is that both sides of the equation are multiplied (or divided) by the same number, and the equation still holds
8. What is an equation? A: an equation with unknowns is called an equation
9. What is a one variable linear equation? A: an equation with an unknown number and the number of times of the unknown number is a one degree equation. Learn the example method and calculation of the equation with one variable. That is, give examples to replace the formula with χ and calculate
10. Fraction: the unit "1" is divided into several equal parts, which represents such a share or fraction
11. The rule of addition and subtraction of fractions: adding and subtracting fractions with the same denominator only adds and subtracts molecules, and the denominator remains the same. Fractions with different denominators are added and subtracted first, then added and subtracted
12. Comparison of fraction size: compared with the fraction of denominator, the larger the molecule is, the smaller the smaller
If the numerator is the same, the larger the denominator is, the smaller the denominator
13. The numerator is the product of the numerator of the fraction and the multiplication of the integer
14. Multiply fractions by fractions, using the product of the multiplication of molecules as the numerator, and the product multiplied by the denominator as the denominator
15. A fraction divided by an integer (except 0) equals the fraction multiplied by the reciprocal of the integer
16. True fraction: a fraction whose numerator is smaller than the denominator is called a true fraction
17. It's called a fraction with a false denominator greater than 1
18. With fraction: write false fraction into integer and true fraction form, called with fraction
19. Basic properties of fraction: the numerator and denominator of a fraction are multiplied or divided by the same number (except 0), and the size of fraction remains unchanged
20. A number divided by a fraction is equal to the number multiplied by the reciprocal of the fraction
Number a divided by number B (except 0) is equal to the reciprocal of number a multiplied by number B
The rule of addition and subtraction of fractions: adding and subtracting fractions with the same denominator only adds and subtracts molecules, and the denominator remains unchanged. Fractions with different denominators are added and subtracted first, then added and subtracted
The multiplication rule of fractions: use the product of molecules as the numerator and the product of denominator as denominator
What is ratio: Division of two numbers is called the ratio of two numbers. For example, the preceding and subsequent terms of the ratio of 2 / 5 or 3:6 or 1 / 3 are multiplied or divided by the same number (except 0), and the ratio remains unchanged
What is proportion: a formula that indicates that two ratios are equal is called proportion, such as 3:6 = 9:18
The basic nature of proportion: in proportion, the product of two external terms is equal to the product of two internal terms
25. Solution ratio: find the unknown term in the ratio, which is called solution proportion. For example, 3: χ = 9:18
26. Positive proportion: two related quantities, one of which changes, and the other follows. If the corresponding ratio (i.e., quotient K) of the two quantities is fixed, the two quantities are called positive proportional quantities, and their relationship is called positive proportional relationship. For example, Y / x = K (k is fixed) or KX = y
27. Inverse proportion: two related quantities, one of which changes, and the other changes with it. If the product of two corresponding numbers in these two quantities is fixed, the two quantities are called inversely proportional quantities, and their relationship is called inverse proportional relationship. For example, X × y = K (k is certain) or K / x = y
Percentage: a number that indicates the percentage of one number to another. It is also called percentage
29. To convert a decimal into a percentage, just move the decimal point to the right by two places and add a percent sign after it. In fact, to convert a decimal into a percentage, you just need to multiply the decimal point by 100%
30. Change the percentage into a decimal. Just remove the percent sign and move the decimal point to the left by two places
31. To convert a fraction into a percentage, usually the fraction is first converted into a decimal (usually three decimal places are reserved when the division is not complete), and then convert the decimal into a percentage. In fact, to convert a fraction into a percentage, you should first convert the fraction into a decimal and then multiply it by 100%
32. Change percentage into fraction, first rewrite percentage into fraction, and reduce offer into simplest fraction
33. Learn how to turn a decimal into a fraction and how to turn a fraction into a decimal
34. Greatest common divisor: if several numbers can be divisible by the same number at one time, this number is called the greatest common divisor of these numbers
Coprime number: two numbers with a common divisor of 1 are called coprime numbers
The least common multiple: the common multiple of several numbers is called the common multiple of these numbers
General division: to convert the fractions of different denominators into fractions with the same denominator that are equal to the original fractions

Mathematical formula of grade one to grade six in primary school

1. The number of copies per copy = the total number of copies △ the number of copies = the total number of copies △ the number of copies = the number of copies 2, 1 times × multiple = several times, several times △ 1 times = several times, 3, speed × time = distance, distance, speed, time, distance, time, distance, time, distance, time, distance, speed, time, distance, time, distance, speed, time, distance, time, distance, time, etc

Mathematical formulas for grades one to six, all

The basic formula of mathematics formula of grade one to grade six of primary school is: 1. Number of each piece × number of copies = total number of copies

The mathematical formula of grade one to grade six in primary school

Number of copies × number of copies = total number
Total number △ number of copies = number of copies
Total number of copies = number of copies
1 times × multiple = several times
Several times △ 1 times = Multiple
Several times △ times = 1 times
Speed x time = distance
Distance △ speed = time
Distance △ time = speed
Unit price × quantity = total price
Total price / unit price = quantity
Total price / quantity = unit price
Work efficiency x working time = total work
Total work △ work efficiency = working time
Total work × working time = work efficiency
Addend + addend = and
Sum - one addend = another
Minuend minus = difference
Minus minus = minus
Difference + subtraction = minuend
Factor × factor = product
Product △ one factor = another
Divisor △ divisor = quotient
Divisor △ quotient = divisor
Quotient × divisor = divisor
Square C perimeter s area a side length perimeter = side length × 4 C = 4A area = side length × side length s = a × a
Cube V volume a edge length surface area = edge length × edge length × 6 s surface = a × a × 6 volume = edge length × edge length × edge length v = a × a × a rectangle C perimeter? S area a side perimeter = (length + width) × 2 C = 2 (a + B) area = length × width s = AB 4 cuboid V volume s area? A length? B width h height (1) surface area (length × width + length × height + width × height) × 2 s = 2 (AB + ah + BH) (2) volume = length × width × height v = ABH triangle s area a base H height area = bottom × height △ 2 s = ah △ 2 triangle height = area × 2 △ bottom triangle bottom = area × 2 △ high parallelogram s area a base h height area = bottom × height s = ah
Trapezoid s area a upper bottom B lower bottom h height area = (upper bottom + bottom) × height △ 2 s = (a + b) × h △ 2 circle s area C circumference Π d = diameter r = radius (1) circumference = diameter ×Π = 2 ×Π? Radius C = Πd = 2 Π R (2) area = radius × radius ×Πcylinder V volume? H height? S; Bottom area? R bottom radius C bottom perimeter (1) side area = bottom perimeter × height (2) surface area = side area + bottom area × 2 (3) volume = bottom area × height (4) volume = side area ÷ 2 × radius
The volume of cone V is h and the height is s; Base area R base radius volume = base area × height △ 3 total number △ total number = average number sum difference formula (sum + difference) △ 2 = large number (sum difference) △ 2 = decimal sum multiple problem and △ (multiple-1) = decimal decimal decimal × multiple = large number (or sum decimal = large number) difference multiple problem difference × (multiple-1) = decimal decimal decimal × multiple = large number (or decimal + difference = large number) tree planting problem The problem of tree planting on an unclosed line can be divided into the following three situations: (1) if trees are to be planted at both ends of an unclosed line, then the number of trees = the number of sections + 1 = the total length of the line × (the number of trees - 1) the total length = the distance between trees × (number of trees - 1) the distance between trees × (number of trees - 1) the total length × (number of trees - 1) if trees are to be planted at one end of the non closed line, the other end should not be planted, Then the number of trees = the number of sections = the total length × the distance between plants = the distance between plants × the number of trees = the total length × the number of trees. (3) if trees are not planted at both ends of the non closed line, Then the number of trees = number of segments-1 = total length × (number of trees) - 1 total length = spacing × (number of trees + 1) spacing = total length × (number of trees + 1) number of trees planted on closed lines is as follows: number of trees = number of sections = total length × total length of spacing = spacing × number of trees = total length × number of trees = total length × (profit + loss) × difference of distribution amount = number of shares participating in distribution (large profit - small profit) × difference of two distribution amount = number of shares participating in distribution (large loss - small loss) × difference of two distribution amount = number of shares participating in distribution meeting distance = speed and × meeting time meeting time = meeting distance △ speed and speed sum = meeting distance △ meeting time and problem tracing distance = speed difference × pursuit time Follow up time = pursuit distance △ velocity difference velocity difference = pursuit distance ／ pursuit time flow problem downstream velocity = still water velocity + water flow velocity countercurrent velocity = still water velocity + countercurrent velocity ＝ (downstream velocity + countercurrent velocity) × 2 flow velocity = (downstream velocity countercurrent velocity) × 2 concentration problem solute weight + solvent weight = solution weight Weight of solute ×weight of solution × 100% = weight of solution × concentration = weight of solute × weight of solute △ concentration = weight of solution, profit and discount problem, profit = selling price cost profit margin = profit × cost × 100% = (selling price ＋ cost-1) × 100% up and down amount = principal × percentage discount = actual selling price ＋ original selling price × 100% (discount ＜ 1) Interest = principal × interest rate × time, after tax interest = principal × interest rate × time × (1-20%)

How to use the sentence patterns of Chinese and English,

Square: perimeter = side length × 4C = 4A area = side length 2S = A2 rectangle: perimeter = (length + width) × 2C = (a + b) × 2 area = ABS = AB triangle: area = bottom × height △ 2S = ah △ 2 parallelogram: area = ahs = ah trapezoid: Area = (Part 1)