How to calculate the final value and present value of advance annuity?

How to calculate the final value and present value of advance annuity?

The final value of the annuity is f = a [(F / A, I, N + 1) - 1] for example: in order to prepare for his son's college education, Mr. Wang deposited 3000 yuan in the bank at the beginning of each year for six consecutive years. If the bank deposit interest rate is 5%, how much can Mr. Wang withdraw the capital and interest at the end of six years? F = a [(F / A, I, N + 1) - 1] = 3000 * [(F / A, 5%, 7) - 1] = 3000 * (8

On the calculation formula of present value of interest paying bonds
Pricing formula of interest bearing bonds
For bonds that pay interest on time, there are two sources of expected monetary income: coupon interest and face value received regularly before maturity. The necessary yield can also be determined by reference to comparable bonds
For bonds that pay interest once a year, the value determination formulas of compound interest discount and simple interest discount are as follows:
P=C/1+r+C/(1+r)^2+C/(1+r)^3+...+C/(1+r)^n+M/(1+r)^n
=∑C/(1+r)^t+M/(1+r)^n
P=∑C/(1+r×t)+M/(1+r×n)
Among them: P -- bond intrinsic value, namely pastes the present value
C -- the interest received each year; m -- the face value; n -- the number of remaining years;
R -- necessary rate of return; t -- the t th time, 0

In other words, a sum of money I get in one year is 100 yuan, but the annual interest is 2.25%. In fact, this money is only worth 100 / 1.0225 yuan, which is 97.8 yuan. That is to say, money in the future is different from money in the present, because money has its time value. Something divided by (1 + R) is something

The bond is valued by a formula
1. Cottonwood issues 5-year pure discount bonds with a face value of US $1000 and a market interest rate of 8%
2. A company issues 8-year bonds with a face value of 1000 yuan, a coupon rate of 7% and a market interest rate of 10%. Please value the bonds

2. Coupon = 1000 * 7% = 70 yuan. Assuming that the interest is paid at the end of each year, the price is 70 / (1 + 10%) ^ 1 + 70 / (1 + 10%) ^ 2 + 70 / (1 + 10%) ^ 3 + 70 / (1 + 10%) ^ 4 + 70 / (1 + 10%) ^ 5 + 70 / (1 + 10%) ^ 6 + 70

Talking about the present value calculation formula
For example:
The present value of the purchase price is 900000 * (P / A, 10%, 10) = 900000 * 6.1446 = 5530140
How to explain this p / a? I'm confused,

Formula in financial management: annuity present value formula
P: Present value
A: Annuity (annuity)
900000 × (P / A, 10%, l0) can be understood as: when the annual interest rate is 10%, 900000 yuan needs to be withdrawn at the end of each year in the next 10 years, and how much money needs to be deposited now

Calculation formula of present value (simple interest and compound interest)
Original formula and examples

Simple interest = principal * interest rate * year
Sum of principal and interest = principal * (1 + interest rate * year)
Compound interest sum of principal and interest = principal * (1 + interest rate) V year
There are many examples, you can find them yourself

According to compound interest, the annual interest rate is 3%. What is the present value of 1000 yuan after three years? How to calculate it? What is the formula

X (1 + 3%), # 179; = 1000
X = 1000 / (1 + 3%) (?) 179; = 915.14 yuan

If the annual interest rate is 10%, what is the final value and present value of 1000 yuan for a three-year ordinary annuity

Final value of annuity f = a [(1 + I) ^ n-1] / I = 1000 * [(1 + 10%) ^ 3-1] / 10% = 1000 * 3.310 = 3310
Or = a (F / A, I, n) = 1000 * (F / A, 10%, 3) = 1000 * 3.310 = 3310 (yuan)
Annuity present value p = a [1 - (1 + I) ^ (- n)] I = 1000 * [1 - (1 + 10%) ^ (- 3)] / 10% = 1000 * 2.4869 = 24869
Or = a (P / A, I, n) = 1000 * (P / A, 10%, 3) = 1000 * 2.4869 = 2486.9 (yuan)

What should I do if I just mix up the formula of final value of compound interest, present value and present value of deferred annuity?

In fact, there are rules to follow. The main purpose of memorizing formulas is to remember coefficients. If you can remember the derivation process, you can remember it by pushing the sequence several times when you have nothing to do
1、 Post paid annuity:
(1) Final value: (F / A, I, n) = [(1 + I) ^ n-1] / I;
(2) Present value: (P / A, I, n) = [1 - (1 + I) ^ - n] / I
Note: the main difference between the two formulas lies in the molecule, except that in the final value n is positive, in the present value n is negative, and there is a negative sign in front of it (although far fetched, it is a way of memory at least);
2、 Advance annuity:
(1) Final value f = a (F / A, I, n) x (1 + I) = a [(F / A, I, N + 1) - 1];
(2) Present value p = a (P / A, I, n) x (1 + I) = a [(P / A, I, n-1) + 1]
Note: if you carefully observe these two formulas and the coefficient formula of the post paid annuity, you will find (of course, you can directly infer it from the definition): if the period number of the final value coefficient of the post paid annuity is increased by 1, the coefficient minus 1 becomes the pre paid annuity; if the period number of the present value coefficient of the post paid annuity is decreased by 1, the coefficient plus 1 becomes the pre paid annuity
3、 Deferred annuity is based on the first two kinds of annuity
4、 Present value of perpetual annuity: it is a simple derivation of infinite period, that is: present value = 1 / I. there is no final value

What's the difference between compound interest final value coefficient, compound interest present value coefficient, annuity final value coefficient and annuity present value coefficient?
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It's all a matter of time value. In short, today's 100 yuan is not equal to the 100 yuan five years later. How much is the 100 yuan five years later equivalent to today's? This requires discount, that is, 100 times the present value coefficient of compound interest of the corresponding interest rate with a maturity of 5. If you want to know how much today's 100 yuan is equivalent to five years later, 100 times

The formula of compound interest present value insertion method
Suppose you buy a bond of a company with a face value of 1250 yuan and a coupon rate of 4.72%. Then you charge 59 yuan of interest every year and buy it with 1000 yuan
59 * (1 + I) minus 1 power + 59 * (1 + I) minus 2 power + 59 * (1 + I) minus 3 power + 59 * (1 + I) minus 4 power + (1250 + 59) * (1 + I) minus 5 power = 1000
I = 10% calculated by insertion method
What's the calculation, please

If this is calculated by hand, we need to use the step-by-step test method. First, let I = 8%, and the left side of your formula = 59 × (P / A, 8%, 4) + (1250 + 59) * (P / F, 8%, 5) = 1086.32
Let I = 12%, 59 × (P / A, 12%, 4) + (1250 + 59) * (P / F, 12%, 5) = 921.93
Interpolation method
（1）1086.32 8％
（2）1000 i％
（3）921.93 12％
(1086.32-1000)/(1086.32-921.93)=(8-i)/(8-12)
I = 10.1% because I keep two decimal places in the previous calculation, so the final result may have some errors, so it's better to keep four decimal places
Interpolation generally needs to know the range of I, otherwise the calculation is very heavy. I know I = 10%, so I use 8% and 12% to test. Of course, if I use 9% and 11% to test, I will be more accurate. You can try it yourself, and the result will be closer to 10%