Фінансова статистика - Shustikov A.A.

10.2. Нарощення за простими відсотками

Pіd naroshchennuyu sumo pozhki rozumіyut pocchatkovu її sumu at once on the basis of non-up to the order of the line pozichki. Process zmіni sumi borgu at once with increasing rates for a simple rate of payments can be affected by the arithmetical progress of P , P + Pi , P + Pi + Pi , etc. The first term is dorivnyu P , rіznitsya Рі , the rest member Is the sum of the borgo S = P + P • i • n .

Suma, scho accumulated up to the line, stored in two elements - pochatkovo sumi borgu ta vіdsotkіv:

S = P + I ,

De I = P • i • n.

Process naroshchenya sumi burgu for forgive vidosotkami is itself a lien deposit of narcotized sums S the same as the line of the posi- tion, which is shown in Fig. 10.1.

Process naroshchennya sumi burgu for forgive vidotsok

Fig. 10.1. Process naroshchennya sumi burgu for forgive vidotsok

The word "forgive" is visible in the graph, it is directly proportional to the positively, the rates of the positives and the line of the posi- tion. Naroka suma viznachaetsya mnozhennyam pochatkoy sumi posychki on mnozhnok naroshchennya, yaky pokazuє, beside skilki razіv susha bіlsha for the ears. The formula for rozraunku polyfactory nasyschennya lie in view of the vikoristovovanoi vidsotkoy rates that minds naroshchennya. Yakshcot with tsiomu vikoristovuyatsya simple vidsotkovaya rate, then naroshchenu sumu pozhki viznachayut for such a formula:

S = P + I = P (1 + ni ).

The value of S is called summed payment, I impose a formula - the formula for naroshchennya for forgive vidosotkami, and the multiplier (1 + ni ) - multiplane naroshchennia.

Attachment 1. A loan was seen from the sum of 1000 UAH. On the lines of 2 rock, 5% of the riches. Necessarily viznachiti vidsotok, yaky otrimuє creditor, that sumu, yaku wrestler vypplatit naprikintsi string.

Rozvjazannya. Spotchatka viznachimo value of the top

І = Pi • n = 1000 • 0,05 • 2 = 100 UAH,

And potim naroshchenu sumu S = P + I = 1000 + 100 = 1100 UAH.

Qiu problem can be solved in the same way:

S = P (1 + ni ) = 1000 (1 + 2 • 0.05) = 1100;

I = S - P = 1100 - 1000 = 100 UAH.

Yakshto rate vіdsotkіv zmіnyuyutsya in an hour, then the formula naroshchennya for simple fіksovannuyu zmіnnymu stakovoy rozrahovuetsya such a rank:

Bid rate ,

De ik - the rate of forgiveness for the period k ; Nk is the triviality of the period k .

Attachment 2. Yaka will be put up with a soup pozhichki, yakshcho in ugodi perebachaetsya for Pershi two rock narahuvannya 10% rіchnih, and in the approaching two rock the rate is simple відсотків збільшується кожні півроку на 1 відсотковий пункт. Початкова сума позички дорівнювала 1000 грн.

Rozvjazannya .

Simple

As a rule, it is simple to be vikorostvuytsya in korotkostrokovyh fisnansovo-credit operations, tobto if the lines of the pose are not transplanted to one rock. Oskilki lines pozichki less than one rock, and vidtsotkova rate vstanovlyuetsya at rozraunku on one rik, vinikaє neobhіdnіst viznachiti, yaka part of vidsootkiv moe bouti paid to the lender. Якщо q - кількість днів корстування грошин stretching to rock; К - кількість днів у році (the base of rock), тодиі of the lines of the korstustannya is very small in the rock n, you can submit it with this rank:

Part of the payment is paid to the creditor .

The values ​​of q and K can be used to increase the numeric values. You can calculate the number of days ( q ) accurately after the calendar for approx., If vvazhayut, sho misyats nezalezhno vіd, skilki dnіv bulo for the calendar, dorivnyuє 30 days.

The purpose is to build a basis for nakrauvannya vidsotkiv, tobto kіlosty dnіv u rotsi. Кількість днів у році можна розрахувати exactly, тобто за календарь (365 або 366 днів), abo approximate, if vvazhayut, scho рік дорівнює 360 днів. Yaksho рік warehousing з 360 днів, then in the case of a given time, the zwachinein abo commercials. Якщо рік дорівнює кількості днів for the calendar, then calculate the exact figures.

Різні znachennya q ta K lead up to rіznyh result in naraahuvannі prostyh vіdsotkіv. For short-line fisansovo-credit operations in this case, you can visco-vivious formula of simple complaints:

Фінансово-кредині операції .

There are three varieties of roses for visitors:

A) zvichaini vidosotki z okolznoyu kilkisty dnіv posychki, if q moe approximate value, and K = 360 dniv. Such a method nahrauvannya vіdsotkіv distav nazvu nimetskogo techniques naraahuvannya vidsotkiv. Він використовується, if not потрібінії гістої accuracy with naryakhvanіі відсотків;

B) commercial services, if q is accurate, and the amount is 360 dniv. Tse method nahrauvannya vidosotkiv naychastisha zastosovuyut with obliku vekselіv that інших операціях у комерційних banks. Tse method nahrauvannya vіdsoтків іноді nazivayut bankovsky, abo french;

C) Precision in the exact position of the day, if q is accurate, and K = 365 dniv. Tse method is the result of finding results. At the practical level, the method is called the Anglic Method of Nursing the Visions.

Іноді прості відсотки mozhut vikoristovovatisya is not short of a short-row, and th dovgostrokovyh operatsiyah, if vidosyka nahachovuyutsya spozhivchomu credit, scho, yak rule, nadaetsya kilka rock.

With the help of a loan, the problem of the value of a one-time repayment payment. Він viznachaetsya, vyhodachi z sumy credit and the values ​​of accrued taxes. Redeem sumy a loan at once with accruals vidsovatyvat rivnimi partnym by extension vsogo a line to the credit. The value of the paying payment ( q ) is calculated for the formula:

Ціна товару abacum loan; ,

De R - the price of a product to a loan; M - payment amount for the рік; N - the lines of credit in rock; І - simple rіchna rate відсотків, під яку loan is imposed; Q - sum of one payment at repayment.

Zastosovoychi taku method of repaying the loan, the actual soup burgu postynno zmenushyutsya, and videsoche zalishayutsya postyynimi extension of the string. Danyu razi dysyna vidsotkova rate for settling a loan viyavlyaetsya bilshoyu, nizh bet for credit for loans.