The final value refers to the future value of monetary funds, that is, the value of a certain amount of funds at a certain moment in the future, expressed as the sum of principal and interest.
The formula for calculating the final value of simple interest: f = p (1+r× n)
The formula for calculating the final value of compound interest is f = p (1+r) n.
Where f represents the final value; P stands for principal; R stands for annual interest rate; N represents the number of interest-bearing years.
Among them, (1+r) n is called the compound interest final value coefficient, and it is denoted as fvr, n, which can be found from the compound interest final value coefficient table.
Calculation of present value
Present value refers to the present value of monetary funds, that is, converting a certain amount of funds into present value at a certain point in time.
Formula for calculating the present value of simple interest:
Formula for calculating the present value of compound interest:
Where p stands for present value; F represents the amount that will happen at a certain time in the future; R stands for annual interest rate; N represents the number of interest-bearing years.
Among them, it is called the compound interest present value coefficient, and it is recorded as pvr, n, which can be found through the compound interest present value coefficient table.
Note: When the interest rate (r) and the number of periods (n) are fixed, the present value coefficient of compound interest and the final value coefficient of compound interest are reciprocal.
pension
Annuity is to receive and pay the same amount at equal intervals in a certain period of time. In economic life, annuity phenomenon is very common, such as equal installment, straight-line depreciation, equal monthly salary, equal cash flow and so on. Annuities are divided into ordinary annuity and early annuities according to the time of occurrence. Ordinary annuity, also known as post-paid annuity, is an annuity that occurs at the end of each period; An early annuity is an annuity that occurs at the beginning of each period.
(1) ordinary annuity final value
Calculate the final value of the amount incurred in each period, which adds up to the final value of the annuity.
Ordinary annuity final value calculation formula is:
Among them, it is called the final value coefficient of annuity, and it is recorded as fvar, n, which can be found through the final value coefficient table of annuity.
(2) The present value of ordinary annuity.
The present value of an annuity is calculated by adding up the amounts incurred in each period.
The formula for calculating the present value of ordinary annuity is:
Among them, it is called the present value coefficient of annuity, and it is recorded as pvar, n, which can be found through the present value coefficient table of annuity.
(3) the final value of early annuity
The calculation of the final value of early annuity is based on the final value of ordinary annuity, and its calculation formula is:
f=a×fvar，n×( 1+r)=a× [fvar，n+ 1- 1]
(4) Present value of advance annuity.
The calculation of the present value of advance annuity is based on the present value of ordinary annuity, and its calculation formula is:
p=a×pvar，n×( 1+r)=a× [pvar，n- 1+ 1]
4. Special annuity
(1) sinking fund
Sinking fund is a bond due after several years of repayment, and a fixed amount of funds must be accumulated every year. In essence, it is the problem of finding an annuity by knowing the final value of the annuity.
Calculation formula of sinking fund: a = f/fvar, n
(2) Average annual investment recovery
The average annual capital recovery is to recover the current investment and recover the same amount of funds every year in the future. Essentially, it is a question of finding an annuity from its present value.
The calculation formula of average annual investment recovery is: a = p/pvar, n.
(3) Permanent annuity
Permanent annuity refers to an indefinite annuity. The permanent annuity has no final value, and its present value is calculated as follows:
P = accounts receivable
(4) Deferred annuity
Deferred annuity does not start from the first period of the first year, but after several periods, an equal amount occurs at the end of each period. The calculation of the final value of deferred annuity is the same as that of ordinary annuity, and there are two methods to calculate its present value:
Methods 1: p = a× (pvar, m+n-pvar, m)
Method 2: p = a× PVAR, n×pvr, m.
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Present value and final value of compound interest, present value and final value of annuity
Compound interest present value coefficient = 1/( 1+I) n = (p/s, i, n)
Where I is the interest rate and n is the duration.
This is a question of finding the present value of future cash flows.
59( 1+r)^- 1 +59( 1+r)^-2 +59( 1+r)^-3 +59( 1+r)^-4 +(59+ 1250)( 1+r)^-5 = 1000
59*(P/A，I，5)+ 1250*(P/F，I，5)= 1000
The first (P/A, I, 5) is the present value coefficient of the annuity.
The second (P/F, i, 5) is the present value coefficient of compound interest.
Usually measured by interpolation.
For example, if I=9%, you will get an answer A, which is greater than1000; Let I= 1 1% and you will get another answer B, which is less than 1000.
There will be (1000-a)/(b-a) = (x-9%)/(11%-9%).
Solve the equation to get x, which is 10%.
The present value coefficient of annuity (P/A, i, n) = [1-(1+i)-n]/i.
Compound interest present value coefficient (P/F, I, n) = (1+I)-n
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The final value of the annuity is the amount you invest every year. Calculated according to the deposit interest rate of 0.72%, you can get it when you deposit it in 10.
For example, if you save 654.38+10,000 yuan every year for 10 years and the annual interest rate is 0.72%, then the final value of your annuity is
10 * (F/A，0.72%， 10)= 10+00 *( 1+0.72)+...+ 10 * ( 1)
The present value of an annuity is calculated in the opposite way, that is, by investing an equal amount of money every year and withdrawing it after 10 at the deposit interest rate of 0.72%, you can get the money. Then, the present value of an annuity refers to how much it is worth today.
For example, if you deposit 654.38 million yuan every year for 65,438+00 years and the annual interest rate is 0.72%, then the present value of your annuity is
10 * (P/A，0.72%， 10)= 10+ 10/( 1+0.72)+...+ 10/( 1)
(For example, to put it bluntly, the final value of an annuity refers to the amount of money you can get from the bank in a few years if you save the same amount of money at equal intervals; The present value of an annuity refers to how much money you must deposit in the bank now if you want to get the same amount of money at equal intervals in the next few years. )
Compound interest final value = present value * compound interest final value coefficient
Compound interest present value = final value * compound interest present value coefficient
Annuity is equal amount+term+series.
The relationship between annuity and compound interest, annuity is the sum of compound interest.
Annuity forms: ordinary (final), immediate (beginning), deferred (with interval) and permanent (without final value).
Ordinary annuity final value = annuity * annuity final value coefficient
Sinking fund annuity = final value/annuity final value coefficient
Ordinary annuity present value = annuity * annuity present value coefficient
Capital recovery = annuity present value/annuity present value coefficient
Immediate annuity final value = annuity * ordinary annuity final value coefficient *( 1+i).
Immediate annuity present value = annuity * immediate annuity present value coefficient (number of periods minus 1, coefficient plus 1)
Deferred annuity is a special form of ordinary annuity.
The three formulas need not be memorized. This is how I understand them!