home Finance Books Фінансова статистика - Shustikov A.A.

Фінансова статистика - Shustikov A.A.

11. WAREHOUSE CABINETS

11.1. Нараування складних річних відсотків

Do довгострокових фінансово-крединих операціях, якщо відсотки не виплачуться відразу після їх нарахування, and приедитьсяться до суми боргу, for сущіння суми poschki застосовуться складні відсотки. The base for ix nahrauvannya not zalishaetsya postynoyu; Вона збільшується з кожним кроко у чаі on the value приєднаних відсотків, начахох у попередньому періоді, and the process of zachatkovyi sumi poskryuyutsya poskchoryuetsya.

Приєднання nrahovanih vіdsotkіv to sumi, yak bula base for їх viznachennya, nazivayut kapitalizatsiyu vіdsotkіv .

Yaksho vidsochki nahachuyutsya one time naprikintsi rock, then in the early rock narodeno suma dorivnyuє Р + Р • і , in кінці other rock - Р (1 + і ) + Р (1 + і ) i = Р (1 + і ) 2, Before the third rock - P (1 + i ) 3. The series is the geometric progress of P , P (1 + i ), P (1 + i ) 2, P (1 + i ) 3, ..., the first member of the anchor point of the positon P , and the denominator is (1 + i ) .

The sum - a member of the geometric progress in the enlarged patch is added. For the n- th rock, the embroidered member of the geometric progression of the matrimony of the V (1 + i ) n , a narrative of the narrative sum of the naprikinsky line of the posi- tion.

Otzhe, naraahuvannya folding vidsotkiv zdіysnjєyatsya for such a formula:

,

De S - summed up payment (borgu), P - porchatkova suma borgu, i - folded rate rate, n - number of perforums naryahuvannya vidoskiv.

The value (1 + i ) n is denoted by the multiplicity of extensions. The value of the multiplicand of extinction for the integers n i is imposed in addendum 1.

1. The loan is given in the amount of 1000 UAH. On 5 rockiv for a folding rate of 10% of the riches. Viznachit, yaku sumu is guilty of turning the wrestler naprikintsi line posychki.

Rozvjana : S = P (1 + i ) n = 1000 (1 + 0.1) 5 = 1610.5 UAH.

Yakshto perebachayutsya zmіni y chasі, ale zastosovuyutsya fіksovany (zmіnnі) rates відсотків, then the formula naroshchennya for folding vіdсотки матиме such viglyad:

S = P (1 + i 1) n 1 (1 + i 2) n 2 ... (1 + ik ) nk ,

De i 1, i 2, ..., ik - the last value of the rates of viscosities; N 1, n 2, ..., n k - the period, in the course of which one gets nahrauvannya for the current rates.

Приклад 2.Відсоткова the rate for the pose is marked on the river 8.5% plus the extra charge of 0.5 points to the point in the first two rockies and 0.75 points of the point - at the onset of three rock.

Розв'язання : Multiplier povyschennya at danyomu raz bude 1,0921,09253 = = 1,549.

Shvidkist zrostane for folding and forgive

Використання у фінансових розрахунках простих і складних відсотків дає неоднакові результатти, відмінність між якими are the lines of a pose. Spivvodnoshennya meaning a lot of narozhnenya daє mozhnivist poryvnyati procesii naroshchennya for the different rates vidsootkiv, albe at absolutely novoevyh values.

The process of the adornment of the burg at the folding rate of payments is done by the shvidche, nizh for a simple rate of viscosities, if there are nuts in the list, I transfer the rik ( n > 1). Yakshcho strings korostuvannya penny n ? 1, then simply give a larger result. The goal is to do the mathematical adjustment of the nerf: n > 1, then 1 + inn <(1 + ic ) n ; N = 1, then 1 + inn = (1 + ic ) n ; If n <1, then 1 + inn > (1 + ic ) n . At tsiomu slid vrahovuvaty odakov base base rock at rozraunkah.

Graphically, the processes of embellishment for folding are clearly visible in Fig. 11.1.

Fig. 11.1. The growth of the embellishment for folding is forgivable

Krivi naroshchennya for forgive those folding vidotskot peretinayutsya in totsi, de lines of the poses dorivnyuet one rock abo one period naraahuvannya vidsoctkiv, toto n = 1 1 + inn = (1 + ic ) n . Portivnemichi process naroshchennya for folding, that is, by the easy rates, you can get a ticket, but you can easily pay a loan to the creditor with a short-stroke pose attached, and folded - with the added settings.

The formula of the

Іноді виникає ситуація, if I can not sing a bag of pennies, or pothiba in Maybutny suma penny in n raziv bilsha. Neophіdno viznachiti, for skіlki rokіv (perіodіv) почакова сума збільшиться у n разів, якщо відома magnitude bankівського відсотка та смови інвестування грошей. In order to isolate the task, vikoristovuyot so zvani form of the subunit, yakі dopomagayut viznachati kilkіst rokіv, for yaki pochatkova suma posychki zbilshitsya in 2 (abo n ) raziv.

Obogalny vipadok, if neobhіdno vysnachiti number of rock, with the extension of some pochatkov suma zbіlshitsya n n разів:

A) for the forgiven people (1 + nin ) = N B) for the folded intersections (1 + ic ) n = N .

N = 2;

А) подвоєння за простими відсотками:

B) podvoyennya for folding vidsotkami:

.

Naryakhuvannya vidsotkiv at dribnomu number of rocks

In vipadkas, if n is not a number, then it is stored in a number of shotguns, narochchenya viznachaetsya dvaam ways: for the formula nasyschenya folding vidostkiv and on the basis of zmishanogo method, zgidno z yakim for the number of rockies narahovuyutsya folding vidoski, and for the shot - simple :

S = P (1 + i ) a (1 + bi ),

De n = a + b , a is the number of rock, b is a shot fragment.

Attachment 3. Loan from rozmіrі 30 тис. UAH Put on lines of 3 rock and 160 dniv. Yaksho obmovlena in the contract, the rate dorivnyuet 6.5% і peredachcheno zmishaniy method nahrauvannya vіdsotkіv, suma borgu na kіniec string stanovitime:

S = 30000 1,0653 (1 + 160/365 0,065) = 37271 UAH.

For the formula nasyschennya folding vidsotkiv

S = 30000 1,0653 1.065160 / 365 = 37252 hrn.