Calculation of annuity Why is there a lot of payment at the beginning of the year?

a = the final value of 100 yuan at the beginning of the first year + the final value of 100 yuan at the beginning of the second year + the final value of 100 yuan at the beginning of the third year + the final value of 100 yuan at the beginning of the fourth year.

b = the final value of 100 yuan at the end of the first year + the final value of 100 yuan at the end of the second year + the final value of 100 yuan at the end of the third year.

The difference between the final value of the two schemes is: the final value at the beginning of the first year = 100 * yuan.

Let's assume that they are all n years, that is, the annuity is paid, the annuity is prepaid, and the annuity is paid in advance, all of which mean the same thing. This happens at the beginning of the period.

Then the beginning of the n+1st time = the end of the nth period, the deadline. One more time, one less than a year.

An ordinary annuity is a postpaid annuity. This happens at the end of the period.

Until the end of the period of the nth time, it is closed. Exactly n times, no more, no less.

Draw an equidistant line segment diagram yourself, and it will be very clear.

The interval between two annuity payments is called the annuity payment period.

End of the n+1st term = Beginning of the nth term.

The term annuity originally meant to refer to a payment that was limited to one payment per year. In fact, many kinds of payments are of the same nature as annuities, except that the unit of time is not limited to one year, so the meaning of the term annuity has now been extended to pay once at every fixed interval.

Whereas, the interval between two annuity payments is called the annuity payment period.

The interval between two adjacent interest-bearing dates is called the interest-bearing period.

The amount paid per pay cycle is an annual amount.

The sum of the annual amounts in each interest-bearing period is called the total annuity of each period.

The period from the beginning of the first payment cycle to the end of the last payment cycle is called the annuity period.

This is the difference between the terminal value of an advance annuity and the terminal value of an ordinary annuity.

The prepaid annuity is paid at the beginning of each year, and the funds paid at the beginning of the first year are calculated for 3 years, the funds at the beginning of the second year are calculated for 2 years, and the funds at the beginning of the third year are calculated for 1 year.

The ordinary annuity is paid at the end of the year, and the interest is calculated at the end of the first year for 2 years, the interest is calculated for 1 year at the end of the second year, and there is no interest at the end of the third year.

The prepayment annuity is paid at the beginning of each period, and the postpayment annuity is paid at the end of the period, and it is obvious that the number of payments is the same by drawing a number line.

This is no problem, so why do you need to charge an extra interest?

Let's say we pay our last annuity now.

- Pay the annuity ——— first

Although the advance payment annuity is paid at the beginning of the period, its final value can only be obtained at the end of the period, so the interest income that this money can bring from the beginning to the end of the period must be counted!

The money is paid at the beginning of the period, but it has not yet reached the end of the period, and the current period has not yet passed, so it can also be counted as interest income for another period. ）

- Postpaid annuity ———

The postpaid annuity is paid at the end of the period, and the final value is obtained without calculating interest.

Therefore, the number of interest-bearing periods of an upfront annuity is one more than that of a post-payment annuity.

The relevant concepts and formulas can be reviewed again, and the number of words I type here may be too crowded, so I won't type.

Hope it helps

Because the prepaid annuity is paid at the beginning of the year, and the later annuity is paid at the end of the year, there is a difference of exactly one year in between. For the final value, isn't paying first a year longer than paying later? Of course, there is one more interest-bearing period.

The prepaid annuity is the cash flow at the beginning of the period, and the postpaid annuity is the cash flow at the end of the period, taking the present value as an example, the present value of the postpaid annuity is to be converted every time the cash flow is converted, but the first cash flow does not need to be converted when the present value of the first annuity is found, because it is zero time, that is, the current cash flow, the present value is itself, and it does not need to be converted, that is, it does not need to calculate interest, and the number of periods is different.

From the perspective of the relationship between the n-period prepaid annuity and the n-period ordinary annuity, the number of occurrences of the two is the same, and the difference is only that the time of the first occurrence is different, resulting in the final value of the n-period prepaid annuity calculating one more period of interest than the final value of the n-period ordinary annuity, therefore, the final value of the n-period prepaid annuity can be calculated by multiplying (1+i) on the basis of the final value of the n-period ordinary annuity.

Advance payment annuity, also known as "advance payment annuity". It refers to the annuity at the beginning of each period.

The so-called ordinary annuity, also known as the "postpaid annuity", refers to the annuity at the end of each period.

Here are some examples:

At the beginning of each year, 50,000 yuan is deposited in the bank, and the principal and interest are fully withdrawn at the end of 2 years. The $50,000 here is an upfront annuity. Assuming that the interest rate is 10% and the interest is calculated with simple interest, the principal amount of 100 000 yuan (50 000 * 2) can be withdrawn at maturity, and the interest can be obtained 15 000 yuan, which is calculated as follows:

The first $50 000:

Interest for the first year = 50 000 * 10% = 5 000 (since it is deposited at the beginning of the year, the interest will be generated at the end of the year).

Interest for the second year = 50 000 * 10% = 5 000 yuan.

The second $50 000:

Interest for the first year = 0 (no interest for the current year because it has not been deposited in the current year).

Interest for the second year = 50 000 * 10% = 5 000 yuan (because it is deposited at the beginning of the year, the interest will be generated at the end of the year).

Let's take a look at the situation of postpaid annuities:

At the end of each year, 50,000 yuan will be deposited in the bank, and the principal and interest will be withdrawn at the end of 2 years. The $50,000 here is an ordinary annuity. Assuming that the interest rate is 10% and the simple interest is calculated, the principal amount of 100 000 yuan (50 000 * 2) can be withdrawn at maturity, and the interest of 5 000 yuan can be obtained, which is calculated as follows:

The first $50 000:

Interest in the first year = 0 (no interest in the current year because it is deposited at the end of the year).

Interest for the second year = 50 000 * 10% = 5 000 yuan.

The second $50 000:

Interest for the first year = 0 (no interest for the current year because it has not been deposited in the current year).

Interest for the second year = 0 (no interest for the current year because it is deposited at the end of the year).

Therefore, it is simply understood that "prepaid annuity" is "first" to pay the principal of the first period than "later paid annuity", that is, if the current annuity is paid at 0:00 at the beginning of the year, the later annuity is paid at 1:00 at the end of the year. Pay the principal early in one installment, and of course charge an extra year of interest.

[Advance annuity: first payment at the beginning of the first year, first payment at the beginning of the second year, and once at the end of the second year (beginning of the third year).]

Attached annuity: Pay once at the end of the first year and once at the end of the second year No, isn't this one more Luo I don't understand the question

If you only purchase an annuity for two years, you can calculate your annuity amount based on the following methods:

1.Start by determining the principal amount you will pay for the annuity, which is the total amount you will pay for the annuity.

2.Then determine the term of your annuity payment, which is the length of time you want your annuity to be paid, usually in years.

3.Finally, based on your principal amount and the limit of the annuity payment period, use the annuity calculation formula to calculate the amount of annuity you can receive each year.

It should be noted that the calculation of annuity involves a number of factors, such as age, gender, interest rate at the time of purchase, etc., so the specific calculation results need to be determined according to your personal fortune and the specific conditions for purchasing an annuity. It is recommended that you consult a professional financial institution or insurance company for more accurate calculations.

You understand the meaning of "present value"!

Can the "1,200 yuan deposited at the end of the first year" and "the 1,200 yuan deposited at the end of the second year" be added together? Can't you add it directly? Can it be added directly? Can't you add it directly? Can it be added directly? Can't you add it directly?

For example, if your salary is 3,000 yuan a month this year, and your salary will still be 3,000 yuan a month in five years, do you think you are willing to continue working? Pigs are willing! - Don't mind the classmates who are staring at the back, I am talking about you, I am talking about pigs.

For example, if you deposit a one-year fixed deposit of 5,000 yuan on January 1 this year, how much can you withdraw by January 1 next year? Bingo, the answer is 5000 (1+RMB.)

So next year's 5,175 yuan, what is its value this year - that is, the current value for short, referred to as the present value - ?

Conversely, 5175 (1+.)

You see, the reverse is the way around, and the result is the same - that is, this year's 5,000 yuan and next year's 5,175 yuan are the same in value, and they are the same.

Therefore, we call "5000 yuan" as the present value of "5175 yuan".

Going back to your book, it's clear that the "$1,200 deposited at the end of each year for 5 years" here is not at the same point in time, so it's best not to simply add them up. The more scientific method is to convert them all to a unified point in time, so you have the following formula: 1200 (1+10%)+1200 (1+10%) 2+1200 (1+10%) 3+1200 (1+10%) 4+1200 (1+10%) 5

1200 (1+10%)—This is the present value of 1200 in the first year, because it is deposited at the end of the year, it needs to be converted to the beginning of the first year, so it should be divided by 1+10%, which is the same as the same reason we used 5175 1+.

1200 (1+10%) 2 - This is the present value of 1200 in the second year, or because it is deposited at the end of the year, it has to be converted to the beginning of the first year, from the beginning of the first year to the end of the second year, 2 years have passed, so it should be divided by (1+10%) 2, that is, divided by (1+10%) to the power of 2.

The same is true for the back (1+10%) 4 and 1200 (1+10%) 5.

Add them all up, which is the sum of the "present value" of the cash deposited in each year.

Understand that wood has? It's a nonsense and meaningless question, but it's even more – where did you get 10 points for this question?