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Fіnansova statistics - Shustіkov AA

11.2. Nomіnalna that efektivnosti rates vіdsotkіv

Yak usually priynyato kapіtalіzuvati vіdsotki not once, but on kіlka razіv Year. Number razіv narahuvannya vіdsotkіv on Year poznachimo lіteroyu m. Rіchna rate vіdsotkіv, yak nazivaєtsya nomіnalnoyu, poznachaєtsya j. Todі in skin okremomu perіodі narahovuєtsya j / m - rate vіdsotkіv. Naroshchennyh scrip viznachayut of the formula:

S = P (1 + j / m) mn.

Butt 4. Credit rozmіrі Nada in 1000 UAH. 5 rokіv pid 12% rіchnih. Vіdsotki on the bag Borg narahovuyutsya schomіsyachno. Neobhіdno viznachiti value Borg naprikіntsі pozichki line.

Rozv'yazannya: S = P (1 + j / m) mn = 1000 (1 + 0.12 / 12) 12 • 5 = 1816.7 USD.

Zbіlshennya m generally produces up bіlsh Shvidky processes of extension. Tse vіdbuvaєtsya fact scho vіdsotki narahovuyutsya chastіshe i REALLY vіdnosny dohіd, yaky otrimuє lender viyavlyaєtsya bіlshim, nіzh nomіnalna rate vіdsotkіv. To dwellers vimіryati efektivnіst tsієї operatsії, vikoristovuyut efektivnosti, abo dіysnu, rate vіdsotkіv, yak vіdobrazhaє that real dohіd, yaky oderzhuyut od odnієї groshovoї odinitsі on Year. Tsya rate pokazuє takozh, yak rіchna rate nadaє that samy fіnansovy result, scho i m -razovі narahuvannya on the Year for the rate j / m.

Efektivnosti rate can know vihodyachi s її viznachennya. Won Oskіlki generally produces before Well fіnansovogo result, scho i bet j / m with m mult narahuvannі vіdsotkіv on Year, then mnozhniki graft on Tsikh rates povinnі Buti rіvnі.

Otzhe can zapisati TAKE rіvnyannya:

(1 + i) n = (1 + j / m) n • m .

Zvіdsi - efektivnosti rate vіdsotkіv viznachaєtsya for with such a formula:

I = (1 + j / m) m - 1.

5. Butt Nomіnalna rate of 6% rіchnih, vіdsotki narahovuyutsya kozhnі pіvroku. Viznachiti efektivnіst tsogo processes of extension.

Rozv'yazannya: i = (1 + j / m) m - 1 = 1.032 - 1 = 6.09%.

Oznachaє Tse, scho pozichka, yak pid nada 6% rіchnih for minds, scho vіdsotki narahovuyutsya two Razi on the Year, brought creditor vіdnosny dohіd rozmіrі at 6.09% on Year. Zamіna in dogovorі nomіnalnoї rate j for narahuvannі vіdsotkіv m razіv on Year on efektivnosti i bet not zmіnyuє fіnansovih zobov'yazan storіn, SSMSC take fate in dogovorі, tobto participant fіnansovoї lands bayduzhe, yak vikoristovuvati rate: 6.09% at abo narahuvannі vіdsotkіv one Year on time, 6% abo narahuvannі vіdsotkіv once on the Year.

Yakscho neobhіdno viznachiti on osnovі efektivnoї nomіnalnu bet, you can vikoristati Taku formula:

j = m ((1 + i) 1 / m - 1).

Tsya situatsіya Mauger viniknuti todі, if the creditor Hoca otrimati dohіdnіst for the Year in rozmіrі i i m narahovuyutsya vіdsotki razіv on Year. Todі Yomou neobhіdno prostaviti in ugodі rіchnu rate vіdsotkіv j.