Зміст:

1 The Rule of 72
2 Factors of 72
3 Сколько лошадиных сил в дельте?
- 3.1 Сколько лошадиных сил в дельте? Ответы пользователей
- 3.2 Сколько лошадиных сил в дельте? Видео-ответы

The Rule of 72

The Rule of 72 is a shorthand method to estimate the number of years required for an investment to double in value (2x).

In practice, the Rule of 72 is a “back-of-the-envelope” method of estimating how long it would take an investment to double given a set of assumptions on the interest rate, i.e. rate of return.

The Rule of 72 is a quick method to estimate the time needed for an investment to double in value.
The Rule of 72 is calculated by dividing 72 by the annualized interest rate (i.e. the rate of return).
Luca Pacioli, an Italian mathematician, is often credited with coming up with the Rule of 72 – albeit, there is uncertainty around its origins.
The Rule of 72 is a reliable approximation intended for “back-of-the-envelope” math, but the estimated number of years is still a mere approximation at the end of the day.

Table of Contents

How to Calculate the Rule of 72
The Rule of 72 Formula
Illustrative Rule of 72 Example
The Rule of 72 Chart
Compound Interest vs. Simple Interest: What is the Difference?
Rule of 72 Calculator
The Rule of 72 Calculation Example
The Rule of 115 Calculation Example

How to Calculate the Rule of 72

The Rule of 72 estimates the time needed to double the value of an investment.

The Rule of 72 is a convenient method to estimate the approximate time for invested capital to double in value.

By merely taking the number 72 and dividing it by the rate of return (or interest rate) expected to be earned, the output is the approximate number of years for an investment to double.

Therefore, the Rule of 72 is a “back of the envelope” estimate of the time to double an investment, yet the method produces a relatively accurate figure.

On that note, using Excel (or a financial calculator) is recommended for a more precise figure, especially in higher stake circumstances.

The Rule of 72 is well-known in finance and is perceived by most as a general rule of thumb to estimate the number of years that it would take an investment to double in value.

Yet, despite the simplicity of the calculation and convenience, the methodology is rather accurate, within a reasonable range.

The Rule of 72 Formula

The formula for the Rule of 72 divides the number 72 by the annualized rate of return (i.e. the interest rate).

Number of Years to Double = 72 ÷ Interest Rate (%)

Thus, the implied number of years for the investment’s value to double (2x) can be approximated by dividing the number 72 by the effective interest rate.

However, the effective interest rate used in the equation is not in percentage form.

Illustrative Rule of 72 Example

For example, if an investor – i.e. a limited partner (LP) of the fund — decided to contribute $200,000 to an active investor’s fund.

According to the firm’s marketing documents, the normalized return should range around 9% approximately, i.e. the 9% is the set return targeted by the fund’s portfolio of investments over the long term (and various economic cycles).

If we assume the 9% annual return is in fact achieved, the estimated number of years for the original investment to double in value is roughly 8 years.

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The Rule of 72 Chart

The chart below provides the approximate number of years for an investment to double.

The left column lists the rate of return – from 1% to 10% – while the right column lists the number of years it would take for the investment to double in value based on the corresponding return.

Compound Interest vs. Simple Interest: What is the Difference?

The Rule of 72 only applies to cases of compound interest, rather than simple interest.

Simple Interest → The accumulated interest to date is not added back to the original principal amount.
Compound Interest → The interest is calculated based on the original principal, as well as the accumulated interest incurred from prior periods (“interest on interest”).

Rule of 72 Calculator

We’ll now move on to a modeling exercise, which you can access by filling out the form below.

The Rule of 72 Calculation Example

Suppose an investment earns 6.0% each year.

Q. Given the 6.0% rate of return, how many years will it take for the value of the investment to double?

If we divide 72 by 6, we can calculate the number of years it would take for the investment to double.

In our illustrative scenario, the investment should double in value around 12 years.

The Rule of 115 Calculation Example

There is also a related but lesser-known rule, called the “Rule of 115”.

Number of Years to Triple = 115 ÷ Interest Rate (%)

By dividing 115 by the rate of return, the estimated time for an investment to triple (3x) can be calculated.

Continuing off the previous example with the 6% return assumption:

Implied Number of Years to Triple (3x) = 115 ÷ 6 = 19 Years

Factors of 72

The factor of a number is the number that divides evenly the given number. Usually when we talk about number factors, we only talk about positive whole factors.

For example, the factors of 10 are 1, 2, 5 and 10. If 10 is divided by any of the numbers 1, 2, 5, 10, the answer will be a whole number:

The factors of a number are any numbers that divide into it exactly, including 1 and the number itself. Number 1 is always the smallest whole factor of the number, the number itself is always the greatest whole factor of the number. So, each number always has at least two factors.

If a number has exactly two factors, 1 and the number itself, this number is called a prime number. Number 1 is not a prime number. The smallest prime number is number 2 (is evenly divisible by 1 and by 2). To write consecutive prime numbers, starting with the smallest, you can use the algorithm sieve of Eratosthenes known before our era. Consider how this algorithm works on the following example.

EXAMPLE: Write down all prime numbers to 72.

SOLUTION: Write a list of whole numbers starting from the smallest prime number 2 to 72.

Circle the number 2 and cross out all numbers that are divisible by 2.

Circle the next number 3 and cross out all numbers that are divisible by 3.

Circle the next number 5 and cross out all numbers that are divisible by 5.

Circle the next number 7 and cross out all numbers that are divisible by 2.

And so on, circle the next numbers and cross out all numbers evenly divisible by this number. All circled numbers are prime numbers from 2 to 72.

A number that has more than two factors is called a composite number.

Ways of finding factors of a number

There are three methods of finding factors of a number:

DIVISION METHOD: the division method is to find all divisors from 1 to the number itself that divide the number without remainder.

MULTIPLICATION METHOD: the multiplication method is to write the number as a product of two numbers in different possible ways.

PRIME FACTORIZATION METHOD: the prime factorization method is to express a composite number as the product of its prime factors.

Division method of finding the factors of 72

Since number 72 is not circled in the example above (algorithm sieve of Eratosthenes), number 72 is a composite number, so it has more than two factors.

We can use division to find all positive factors of 72 (start with 1, then check 2, 3, 4, 5, 6, 7, 8, 9, etc. up to 36 (number 36 is exactly half of 72) and the number 72 itself):

Therefore, 72 has a total of 12 positive factors: 1, 2, 3, 4, 6, 8, 9 12, 18, 24, 36, and 72.

Multiplication method of finding the factors of 72

Represent the number 72 as a product of two numbers in all different possible ways:

All the numbers that are used in these products are the factors of 72. Thus, the positive factors of 72 are 1, 2, 3, 4, 6, 8, 9 12, 18, 24, 36, and 72.

Prime factorization method of finding the factors of 72

Prime factorization is a way of expressing a number as a product of its prime factors. For example,

is not the prime factorization of 72 as number 6 is not a prime number.

is the prime factorization of 72 as numbers 2 and 3 are prime numbers.

There are two possible ways to express number as a product of prime factors:

PRIME FACTORIZATION USING DIVISION METHOD

The division method can be used to find the prime factors of a number by dividing the number by prime numbers. To find the prime factors of a number using the division method complete the next steps:

STEP 1: Evenly divide the number by the smallest possible prime number.

STEP 2: Evenly divide the quotient of step 1 by the smallest possible prime number.

STEP 3: Repeat step 2, until the quotient becomes 1.

LAST STEP: Multiply all the prime factors that are the divisors.

EXAMPLE: Write the prime factorization of the number 72 using the division method.

SOLUTION:

STEP 1: The smallest possible prime number that evenly divides 72 is number 2. Divide 72 by 2:

STEP 2: The smallest possible prime number that evenly divides the quotient 36 is number 2. Divide 36 by 2:

STEP 3: The smallest possible prime number that evenly divides the quotient 18 is number 2. Divide 18 by 2:

STEP 4: The smallest possible prime number that evenly divides the quotient 9 is number 3. Divide 9 by 3:

STEP 5: The smallest possible prime number that evenly divides the quotient 3 is number 3. Divide 3 by 3:

LAST STEP: Multiply all the prime factors that are the divisors:

You can rewrite this prime factorization in the exponent form:

REMARK: Usually this process is not described for so long, but depicted in the form of a column as shown below.

Prime factorization of 72=22233

PRIME FACTORIZATION USING FACTOR TREE METHOD

A factor tree is a special diagram, where we draw the factors of a number, then the factors of those factors and so on until we get only prime factors.

EXAMPLE: Draw a factor tree for the number 72.

SOLUTION: From the multiplication table we know that 72=8×9. Therefore,

Each of these numbers we can represent as products of prime numbers:

So, the final factor tree is

and the prime factorization of 72 is 2×2×2×3×3 or 2332.

and see that that the prime factorizations for all factor trees are the same. This is provided by the Fundamental Theorem of Arithmetic which states that

every natural number greater than 1 can be written as a product of prime numbers, and that up to rearrangement of the factors, this product is unique.

To find the prime factors of a number using the factor tree method complete the next steps:

STEP 1: Draw a factor tree starting from arbitrary numbers with product equal to the given number but finishing with only prime numbers.

STEP 2: Multiply all the prime factors that appear in this factor tree.

The method of finding the factors of a number using the prime factorization of the number is to multiply arbitrary combinations of prime factors.

EXAMPLE: The prime factorization of 72 is 2332. Write down all positive factors of 72 using the prime factorization method.

SOLUTION: To write down all the factors and not lose any, use the following guidance of writing combinations:

first, write down all possible powers of the first prime factor (starting with exponent of 0 and finishing with the maximum possible exponent defined in the prime factorization of the number):

20=1, 21=2, 22=4, 23=8

then write down all possible powers of the second prime factor (starting with exponent of 0 and finishing with the maximum possible exponent defined in the prime factorization of the number):

and then all possible products of powers of both multipliers

Therefore, the list of all 12 positive factors of 72 written in ascending order is

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

Note that only 2 and 3 are prime factors of 72.

Finding the number of positive factors

Using the prime factorization of a number, we can find the number of factors of this number. To do this, complete the following steps:

STEP 1: Write the prime factorization of a number in the exponent form.

STEP 2: Add one to each of the exponents.

STEP 3: Multiply all obtained numbers. This product denotes the number of factors of a number.

EXAMPLE: Find the number of factors of 72.

SOLUTION: From the previous topic, the prime factorization of the number 72 in the exponent form is 2332.

Add 1 to each exponent:

and multiply the obtained sums:

Therefore, the number of factors of 72 is 12.

Positive factor pairs of 72

A factor pair of a number is a set of two factors, which, when multiplied, give this number as a product. For example, factors 5 and 8 form a factor pair of 40 because

EXAMPLE: List all factor pairs of 72.

SOLUTION: Start with 1. Since 72=1×72, put 1 at the beginning of the list and 72 at the end of the list. Factors 1 and 72 form the first factor pair of 72.

Now, try 2. Since 72=2×36, put 2 at the beginning of the list (after 1) and 36 at the end of the list (before 72). Factors 2 and 36 form the second factor pair of 72.

Then, try 3. Since 72=3×24, put 3 at the beginning of the list (after 2) and 24 at the end of the list (before 36). Factors 3 and 24 form the third factor pair of 72.

Continue with 4. Since 72=4×18, put 4 at the beginning of the list (after 3) and 18 at the end of the list (before 24). Factors 4 and 18 form the fourth factor pair of 72.

Check the next factor 6. Since 72=6×12, put 6 at the beginning of the list (after 4) and 12 at the end of the list (before 18). Factors 6 and 12 form the fifth factor pair of 72.

At last, 72=8×9. Two middle factors are 8 and 9. These two factors form the last factor pair of 72.

There are no more whole numbers between 8 and 9 so we are done!

We can graphically represent positive factor pairs as shown below.

Negative factors of 72

From the previous topic you can see that there are 6 factor pairs of 72. All these pairs consist of positive whole numbers.

If we note that the product of two negative numbers gives a positive number, then the same pairs of negative numbers will also be factor pairs.

Therefore, negative factor pairs are

and list of negative factor pairs is

Here two numbers colored in one color form a negative factor pair.

Quiz

SOLUTION: Number 72 has only two prime factors: 2 and 3. The product of these two numbers is 2×3=6.

ANSWER: 6

SOLUTION: Number 72 has 12 positive factors: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72. Factors 2 and 3 are prime factors, factor 1 is neither prime nor composite number, so there are 9 composite factors of 72:

4, 6, 8, 9, 12, 18, 24, 36, 72

The mean number is the sum of all numbers divided by the number of numbers. Therefore, the mean of all composite factors of 72 is

ANSWER: 21

SOLUTION: Number 72 has 12 positive factors: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72. The sum of these factors 1+2+3+4+6+8+9+12+18+24+36+72=195.

ANSWER: 195

a) The sum of all factors of 72 is 0.

b) The product of all factors of 72 is 0.

c) Number 72 has 24 factors.

d) Number 72 has 6 factor pairs.

SOLUTION: Number 72 has 24 factors: 12 positive and 12 negative. So, statement c) is true.

Positive factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

Negative factors of 72: -1, -2, -3, -4, -6, -8, -9, -12, -18, -24, -36, -72.

The sum of all these factors is 0 because the sum of positive and corresponding negative factor is 0 and the sum of twelve zeros is zero too. Therefore, statement a) is true.

Statement b) is false. The product of numbers is 0 when one of these numbers is 0. The number 0 is not a divisor of the number 72, so the product of the factors of the number 72 can not be equal to 0.

Statement d) is false too because the number 72 has 6 positive factor pairs and 6 negative factor pairs, 12 factor pairs in total.

ANSWER: a) True

SOLUTION: A factor pair of a number is a set of two numbers whose product is equal to this number.

Since -12-4=48≠72, numbers -12 and -4 do not form a factor pair of 72 although both of these numbers are divisors of 72.

Conclusions

Most often we are interested only in the positive factors of a number.
Sometimes negative factors have some mathematical interest.
We are never talking about fractional factors of a number.
The number of factors of a number is the same as the number of prime factors of this number only if given number is a prime number.
The number of factors of a composite number is always greater than 2.
All natural numbers are the product of at least one factor pair.
Number 1 is a factor of every natural number.
When dividing, a divisor and a quotient always form a factor pair.
A non-square number has an even number of factors.
A square number has an odd number of factors.

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Factors of 72
“Factors of 72”. Helping with Math. Accessed on March 9, 2024. https://helpingwithmath.com/factors-of-72/.
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Additional Factors Theory:

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Сколько лошадиных сил в дельте?

У нас есть 31 ответов на вопрос Сколько лошадиных сил в дельте? Скорее всего, этого будет достаточно, чтобы вы получили ответ на ваш вопрос.

Сколько лошадиных сил в дельте 72 куба?
Сколько лошадиных сил в дельте 110?
Какой расход топлива на дельте?
Сколько едет Дельта 110 кубов?
Сколько едет мотоцикл Дельта?
Сколько едет мопед Альфа 110 кубов?
Сколько едет Дельта 50 кубов?
Сколько лошадиных сил в мопеде?
Сколько едет альфа 72 куб?
Сколько весит Дельта?
Сколько лошадиных сил в дельте? Ответы пользователей
Сколько лошадиных сил в дельте? Видео-ответы

Сколько лошадиных сил в дельте 110? . Он имеет систему охлаждения воздушную, его рабочий объём составляет 107 кубических сантиметров. Запускается двигатель при .

Сколько лошадиных сил в дельте 72 куба?

Показатели номинальной мощности данного агрегата составляют 6 л. с. при 7500 оборотах за минуту.

Сколько лошадиных сил в дельте 110?

Он имеет систему охлаждения воздушную, его рабочий объём составляет 107 кубических сантиметров. Запускается двигатель при помощи кикстартера или электрического стартера. Мощность составляет мотора 72 лошадиных сил.

Какой расход топлива на дельте?

Расход топлива Дайхатсу Дельта составляет от 8.6 до 11.1 л на 100 км. Daihatsu Delta выпускается со следующими типами топлива: Бензин Regular (АИ-92, АИ-95).

Сколько едет Дельта 110 кубов?

Двигатель объемом 110 куб. см с воздушной системой охлаждение в сочетании с четырехступенчатой механической коробкой передач развивает максимальную мощность 7,0 л. с. Максимальная скорость мопеда не более 80 км/час.

Сколько едет мотоцикл Дельта?

Максимальная скорость 75 км/ч Объем бака 3.5 л Расход топлива 1.6 л/100 км

Сколько едет мопед Альфа 110 кубов?

Объём двигателя составляет 110 кубических сантиметров. Двигатель мощностью 7 л. с. работает мягко, при этом достаточно быстро набирает обороты и на ровной дороге разгоняет до 75 км/ч.

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Максимальная скорость 75 км/ч Объем бака 3.5 л Расход топлива 1.6 л/100 км Рекомендуемое топливо 92-95 АИ

Сколько лошадиных сил в мопеде?

Мопе́д — транспортное средство с двигателем внутреннего сгорания рабочим объёмом не более 50 кубических сантиметров (так же электродвигателем или мотор-колесом мощностью от 250 Вт до 4 кВт) и максимальной конструктивной скоростью не более 50 км/ч (согласно российским Правилам дорожного движения; в других странах могут .

Сколько едет альфа 72 куб?

Объём цилиндра двигателя равен 72 см3. Максимальная скорость, которую развивает мопед Альфа 72 кубика равна 93 км/ч. Привод цепной.

Сколько весит Дельта?

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Сколько лошадиных сил в дельте? Ответы пользователей

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Показатели номинальной мощности данного агрегата составляют 6 л.с. при 7500 оборотах за минуту. Приводить мопеда Дельта 72 сс в действие можно как с помощью .

Мощность 3 л.с. Рабочий объем 49.9 см³; Тип подачи Карбюратор; Тип двигателя 4-х тактный; Количество цилиндров 1; Система охлаждения Воздушное. Трансмиссия:.

Модель – Дельта Тип двигателя – 4-х тактный. Объем двигателя, см³ – 48. Трансмиссия – 4-х ступ. коробка передач с механ. сцеплением. Мощность, л.с. – 4.5

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Объем у двигателя мопеда Delta соответствует всем стандартам – 49,0 куб. см. хотя в некоторых модификациях могут встречаться двигатели и с гораздо большим объемом. Мощность стандартного двигателя составляет 3,5 лошадиных сил, что вполне достаточно для начинающего.

Объём двигателя, 50 куб. см ; Пуск, Электро/кикстартер ; Мощность двигателя, 5 л. с. ; Тормозная система, Барабанная ; Подвески (передняя; задняя), Телескопическая .

Объем двигателя составляет 50 см. куб., а мощность равняется отметке 5 л.с. Такие характеристики мотора схожи с простыми скутерами или более .

Он оснащался мотором 1,3 л. с., развивал максимальную скорость 40 км/ч. Ранние модели оснащались двигателем Д-8[4], самые распространённые двигатели — Д-8Э, .

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Об авторе

Иван Быстров

Здравствуйте! Меня зовут Иван Быстров, и я главный редактор этого сайта. Мне 32 года, я живу в Ярославской области России. Я всегда увлекался автомобилями, всегда хотел узнать больше, но зачастую не мог найти ответы на свои вопросы. Это сподвигло меня на создание проекта, где будет собрано воедино максимальное количество вопросов про автомобили, и на каждый из них будет предложен грамотный ответ! Очень надеюсь, что мой труд поможет всем получить новые знания быстро и без лишних затрат энергии!

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Скільки важить Дельта 72