Financial Management Ordinary Annuity Present Value Formula Please analyze it by a master

It should be a one-time deposit of 37,910 yuan at the beginning of the first year to get 10,000 yuan at the end of each year.

The formula for the present value of annuities is as follows:

1. The formula for calculating the final value of annuity is: f=a*(f a, i, n)=a *(1+i)n-1 i where (f a, i, n) is called "annuity terminal value coefficient."

2. The formula for calculating the present value of annuity is: p=a*(p trace Zen a,i, n)= a*[1-(1+i)-n] i where (p a,i, n) is called "annuity present value coefficient."

Extended information: If the number of annuities n is large, it is obviously quite cumbersome to calculate the present value using the above method. Since the annual payments are equal and the coefficient for converting the present value is regular, a simple calculation method can be found.

Present Value of Advance Annuity:

It is the sum of the principal and interest at the end of the last period, which is equivalent to the compound present value of the equal amount of receipts and payments at the beginning of each period.

The sum of the same. The number of receipts and payments is the same as that of the n-term prepaid annuity, but due to the different payment time, the present value of the n-term prepaid annuity is more than the present value of the n-term ordinary annuity to calculate the interest of one more period. Therefore, the denominator is multiplied by (1+i) on the basis of the present value of the n-period ordinary annuity.

Add 1 to get the present value of the n-installment prepaid annuity.

The formula is as follows: 1. The formula for calculating the final value of annuity is: f=a*(f a,i,n)=a*(1+i)n-1 i, where (f a,i,n) is called "annuity terminal value coefficient".

2. The formula for calculating the present value of annuity is: p=a*(p a,i,n)=a*[1-(1+i)-n] i, where (p a,i,n) is called the "present value coefficient of annuity".

The formula is as follows: 1. The formula for calculating the final value of annuity is: f=a*(f a,i,n)=a*(1+i)n-1 i, where (f a,i,n) is called "annuity terminal value coefficient".The table of the final value coefficient of the ordinary annuity can be checked.

2. The formula for calculating the present value of annuity is: p=a*(p a,i,n)=a*[1-(1+i)-n] i, where (p a,i,n) is called "annuity present value coefficient".A table of the present value coefficients of ordinary annuities can be checked.

The present value of an annuity is usually the annual investment income.

is the present value of the compound interest of the payments received and paid at the end of each period over a certain period of time.

The sum of the same. Annual income of 1 yuan, annual interest rate.

is 10% for a period of 5 years, and the present value of the annuity and annuity in the above example can be calculated as follows:

The present value of 1 yuan in 1 year = yuan).

The present value of 1 yuan in 2 years = yuan).

The present value of 1 yuan in 3 years = yuan).

The present value of 1 yuan in 4 years = yuan).

The present value of 1 yuan in 5 years = yuan).

The present value of 1 annuity for 5 years = yuan).

The general formula for calculating the present value of an ordinary annuity is:

p=a/(1+i)1+a/(1+i)2…+a/(1+i)n，(1)

Multiplication on both sides of the equation (1+i).

p(1+i)=a+a/(1+i)1+…+a/(1+i)(n－1)，(2)

2) formula minus (1) formula.

p(1+i)-p=a-a (1+i)n, and the rest is processed as above.

The present value of the annuity after n periods of 1 yuan and the interest rate is i, which is recorded as (p a, i, n), and the present value coefficient of the annuity can be checked.

Table. In addition, the formulas for calculating the terminal value and present value of prepaid annuities, deferred annuities, and the present value of perpetual annuities can be compared with the above derivation methods to obtain their general formulas for calculating mountain sales.

No, the formula for calculating the present value of an ordinary annuity is: p=a (p a,i,n).

Knowing the present value of p=100,000 yuan, i=8%, n=4 years, find the ordinary annuity a: a=100,000 (p a,8%,4)=100,000 yuan, that is, the installment at the end of each year.

It is recommended that candidates must be familiar with the textbooks, understand the basic knowledge, basic principles, macro theories and basic methods of the textbooks when learning financial management. When candidates solve the question, they should first carefully read the meaning of the question and all the alternative answers, and there are generally three common methods when solving the problem: before studying, let's do a small test, click on the test whether I am suitable to learn and book accounting.

1) Direct selection method. These questions are generally prescriptive "should know" or computational questions. As long as the test takers grasp the test points of the knowledge in the textbook, they can directly make the correct choice or choose the correct answer through calculation.

2) Ambiguous elimination method, that is, the incorrect or incorrect options in the alternative answers are deleted, and the correct answer is selected from the remaining options.

3) Guessing method, you can choose to guess when you encounter a question that you really can't, because you don't get points for choosing a single choice question or a multiple choice question, and the result of choosing the wrong question is the same as not choosing it. However, for true/false questions, because the scoring criteria is the score for judging correctly, no points will be deducted if no judgment is made, and points will be deducted if the judgment is wrong, so it is not appropriate to use the guessing method.

In 2016, Hengqi Education initiated the establishment of the "Industry Management Accounting Research Center" with ** University of Finance and Economics and China Accounting News, which is committed to the research of management accounting in popular subdivided industries.

The present value of annuity is the present value of the equivalent par amount calculated by considering the time value of money when the future value, interest rate (here we default to the annual interest rate) and the number of interest-bearing periods n of the equal amount of receipts and payments.

The formula for the present value of annuity is: (p a,i,n)=1 i-1 [i(1+i) n]. where i represents the annual interest rate, n represents the number of periods, p represents the present value, and a represents the annuity.

The present value of an annuity is the inverse of the final value of an annuity.

Calculation formula: p=[1-(1+i)-n power] i, p is the present value factor of annuity, let the present value of annuity with an ordinary annuity of 1 yuan and the interest rate of i, n periods, denoted as (p a, i, n).

Derivation process: ......

Multiply the equation by (1+i), then:

Then: i) PPA

a(1i)p(1

ia[1i)]

1. Formula of the present value coefficient of ordinary annuity: p a=1 i -1 i(1+i) n; where i represents the rate of return, n represents the number of periods, p represents the present value, and a represents the annuity.

2. For example, if you deposit 1,200 yuan in the bank at the end of each year, for 5 consecutive years, the annual interest rate is 10%, and the present value of the funds you have deposited in the past 5 years

p a =1200 (1+10%)+1200 (1+10%) 2+1200 (1+10%) 3+1200 (1+10%) 4+1200 (1+10%) 5 or =1200*(1 (1+10%)+1 (1+10%) 2+1 (1+10%) 3+1 (1+10%) Mori slag 4+1 Yezen (1+10%) 5)=

The above (1 (1+10%)+1 (1+10%) 2+1 (1+10%) 3+1 (1+10%) 4+1 (1+10%) 5) = is the present value factor; present value = 1200*[1- (1+10%) 5) ]10% =1200*;

3. The present value of annuity is the present value of the equivalent par amount calculated by considering the time value of money when the future value, interest rate (here we default to the annual interest rate) and the number of interest-bearing periods n of the equal amount of receipts and payments.

1. The formula of the spine coefficient of the present value of ordinary annuity: p a=1 i -1 i(1+i) n; where i represents the rate of return, n represents the number of periods, p represents the present value, and a represents the annuity.

2. For example, if you deposit 1,200 yuan in the bank at the end of each year, for 5 consecutive years, the annual interest rate is 10%, the present value of the funds you have deposited in the past 5 years:

p a =1200 (1+10%)+1200 (1+10%) 2+1200 (1+10%) 3+1200 (1+10%) 4+1200 (1+10%) 5 or =1200*(1 (1+10%)+1 (1+10%) 2+1 (1+10%) 3+1 (1+10%) 4+1 (1+10%) 5)=

The above (1 (1+10%)+1 (1+10%) 2+1 (1+10%) 3+1 (1+10%) 4+1 (1+10%) 5) = is the present value factor; present value = 1200*[1- (1+10%) 5) ]10% =1200*;

3. The present value of annuity is the present value of the equivalent face value of these receipts and payments to the present value calculated when the future value, interest rate (here we default to the annual interest rate) and the number of interest-bearing periods n, considering the value of money and time.