Formulas of the interest and equivalence

1) Interest semplice:

In the case of the simple interest, the interest to pay on the debit is proporziona them to the period of time for which the is taken to loan somma. = P * n * i

 

2) Interest composto:

It is the case in which the loan protrae for various interest periods, while the interests come calculate you to the end of every period, if the debtor decides to pay the interests to the end of the loan, are spoken about compound interest in how much mature the interests on the interests.

 

3) Cash flow netto:

It is the arithmetical sum of the entrances and the escapes that are taken place at the same moment of the time.

 

4) Factor of composed capitalization for a single payment :

Draft of a factor that given the understood one they begins them that she comes invested to a data interest rate i, concurs to determine the understood one them that it will come given back to us after n interest periods. In formule

 

5) Factor of update for a single payment :

Draft of a factor that given mounting the final F of a loan, is in a position to characterizing the value begins them that it comes invested to a data interest rate i. In formule

 

6) Factor of capitalization composed for one series of equal payments:

Draft of a factor in a position to determining the mounting F, of one series of equal payments To.

In formule is gained writing F as sum of the single deposits To multiplies to you for (1 i)ⁿ that of it gives the value after n years, writes an other equation then multiplying the previous one for (1 i), finally embezzling member to member obtains the result.

 

7) Factor of the installments of amortization for one series of equal payments:

Draft of a factor in a position to determining the value of the payments of year-end To, necessary in order to form one sum future F. In formule

 

8) Factor of recovery of understood them of one the series of equal payments:

It is a factor that is applied to the case in which a sum is poured and for n years equal ones are received of the installments all that extinguish the prestito. In formule , are gained replacing in 7) the F = P (1 i)ⁿ .

 

9) Factor of update for one series of equal payments:

It is a factor that is applied to the case in which the present value is wanted to be known them to pour in order to obtain to expiring of every interest period one sum always equal A. In formule

 

10) Difference and relation between effective interest rate and nominal interest rate:

If the effective interest rate is as an example 3% on quarterly base then the correspondent nominal interest rate anniversary r it is given from the product of the quarterly effective interest rate for the n° of the present trimesters in a year while the effective interest rate anniversary holds account also of the interests that mature on the interests. The 2 values are legacies from the formula : where :

m is the number of present periods of capitalization in a year

r is the annual nominal rendering

l is the mutual one of the duration in years of the period of capitalization.

 

Calculation of equivalence

11) Meant of equivalence:

Equivalence concurs to bring back the cash flows to the same year being concurred therefore to establish if a solution is more profitable than an other.

 

12) Principles of equivalence:

to)    the equivalent cash flows they are those that have the same value if reported to one same moment.

b)    period must be held account also of the various enforced interest rates in a data.

 

13) Obligation:

Draft of an instrument financial for which who lend of the moneies is come ricompensato with a semiannual coupon or anniversary sin when the restitution of the loan does not happen.

 

14) Rendering upon maturity of one obligation or effective yield:

Draft of the rate of return gained from the obligation from the running date until upon maturity of the same, such rendering is legacy at the price of purchase of the same obligation that if he is inferior to the noun concurs an additional gain. Such rendering is obtained uguagliando the expense for the purchase of the obligation to the present value them of the previewed future entrances.

 

15) Rate coupon one obligation or current yield of one obligation:

It is the relationship between the value of the coupon that the obligation supplies and the price to which the obligation is acquired.

 

16) Loan or mutuum:

Draft of an agreement between a debtor and an creditor in which the sum of money is settled down lend and the modality of reimbursement.

 

17) Mutuum â? add - on â?:

Draft of a mutuum in which the interest comes a priori established, added to the sum to pay, and the all subdivided one for the n° of installments on which the reimbursement is wanted to be distributed.

 

18) Like knitting a mutuum:

Only solution is the possibility to knit a mutuum before its expiration being engaged itself to pay the installments remaining in one. The value of the balance can be calculated in the 2 following ways :

to)    the value of the figure lend in the year is estimated in which it is decided to knit and from such value the value of the installments until then poured is embezzled.

b)    Famous that is the installment and the value of remaining to pay the value of the understood one can be calculated begins them them.

 

19) Understood them circulating clearly:

Draft of the running activity or short period of one enterprise less its running passivities.

Calculation of equivalence and inflation

20) Price index:

It is the relationship between the price of a good or service in a moment of the time and its price in a previous moment.

 

21) medium Rate inflation anniversary:

One uses laddove the periods of reference are more than a year then instead considering the inflation rate year for year if of it it considers one that better approximates every year. IPC _t( 1 f )ⁿ= IPC _{t n}is had that for n=1 supplies the rate inflation anniversary.

 

22) Purchasing power:

Draft of the relationship between the IPC in a year base and the IPC in the year in which estimating the purchasing power.

 

23) Rate anniversary of lessening of the purchasing power:

It is a value similar but not equal to the medium rate of inflation and can be calculated from the relation :

Purchasing power _t * (1-k)ⁿ = Purchasing power_{t n}

 

24) Relation between rate anniversary of lessening of the purchasing power and rate medium anniversary of inflation :

 

25) Interest rate of mercato:

Draft of the interest rate really applied from the market in how much congloba is the reddituale power of the money that the inflation.

 

26) Interest rate deflazionato:

It is the reddituale ability to the money once detratti the effects of the inflation.

 

27) Relation between interest rate of market and interest rate deflazionato:

They are legacies from the inflation rate f, in formulas have :

 

28) Dollars correnti:

They are the dollars that are received or they are yielded in every moment in the time.

 

29) Like passing from running dollars in a year to running dollars in a successive year:

It is necessary to multiply for factor (1 i)ⁿ .

 

30) constant Dollars i':

It is the hypothetical purchasing power of future incomes and expenditures in terms of purchasing power in dollars of a sure year base.

 

31) Like passing from constant dollars in a year to constant dollars in a successive year:

It is necessary to multiply for factor (1 i')ⁿ .

 

32) Relation between running dollars and dollars costanti:

In order to pass from dollars currents to constant dollars of the same year :

Running dollars = (1 f)ⁿ (constant dollars) being f the inflation rate and n the distance in years from the year base.

 

33) Analysis to constant dollars:

It is necessary to tramutare the dollars from currents to constants after which to use the deflated interest rate i'.

 

34) Effects of the change between currencies:

In the change a yield made in a country whose currency is devaluated is an inferior yield to what it would be had otherwise.

Bases for the comparison of the alternatives

35) Base for the comparison:

It is an index that contains information detailed on the series of the entrances and of the escapes that characterize one investment opportunity.

 

36) Present value them or present:

Equivalent to the present time is a clean sum that represents the difference between the equivalent of the escapes and the equivalent of the entrances of the cash flow of an investment for a particular interest rate.

In short consists in bringing back all the cash flows to the year base.

 

37) annual Equivalent:

It is the difference between the annual equivalent of the entrances and the annual equivalent of the escapes of a cash flow.

Is therefore a redistribution on n installments of the understood one begins them them correspondent to the present value them of the data cash flow.

 

38) future Value:

It is the difference between the equivalent entrances and escapes in one same future moment. is therefore mounting between n years had the understood one begins them them correspondent to the present value them of the data cash flow.

 

39) inner Rate rendering:

It is the interest rate that uguaglia the entrances and the escapes equivalents of a cash flow. It can be estimated like that value of the interest rate that renders the present value null them.

 

40) Scope and operation of test 1:

It establishes if a cash flow characterizes a single TIR on condition that you respect the 3 conditions :

to)    F₀ < 0 that is 1° the cash flow must be one exited

b)    Us it must be a single change of sign

c)    PW(0) > 0 that is the sum of all the entrances must be greater of the sum of all the escapes

 

41) Scope and operation of test 2:

Stabilisce if a cash flow with multiple changes of sign characterizes a single TIR on condition that you respect the 2 conditions :

to)    F₀ < 0 that is 1° the cash flow must be one exited

b)    Once characterized a TIR must be had that the part not recovered of the investment, must be always negative except in t = n, where U_n = 0

 

42) Payback without interests:

It is the interval of time necessary in order to recover the set-up cost them of an investment with the net cash flow produced from that investment when the interest rate is equal to 0, is that is the such minimum n that .

 

43) Payback with interests:

It is the interval of necessary time because the equivalent of the entrances of the investment exceeds the equivalent of expenses for the understood one them, is that is the such minimum n that .

 

44) economic Amortization of the understood one them:

It is the constant annual cash flow, for the duration of the investment, equivalent to the cost of the investment represented from the expenditure begins them to clearly of the eventual value of I realize. In short the sum of purchase is distributed on n installments and the sum of sale distributed on the same n installments is embezzled.

 

45) Profile of case of the plan:

It is a temporal profile that measure the equivalent amount clearly in dollars invested or dedicated to the plan in every moment of the time, for all the duration of the cash flow.

for T = 0, 1, 2..., n

Decisional process between various alternatives

46) MARR:

It is the minimal test of rendering of an investment, if our activity gives an inferior MARR to us to the rendering offered from the banks is more convenient to invest in the alternative ânon investireâ?.

 

47) Typology of the investment plans:

to)    Independent

b)    Mutually excluding

c)    Conditions to you

 

48) Base of the decisional criterion:

It is necessary to estimate the economic convenience of the cash flow that gushes from the difference between the cash flows of 2 mutually excluding alternatives.

 

49) Criteria of appraisal of the economic convenience:

to)    Present value calculated they on the investment increase them

b)    inner Rate rendering on the investment increases them

c)    Present value calculated them on the investment total

 

50) Criterion of the present value calculated them on the investment increases them:

Currency the present value them of the cash flow difference of the flows To₁ and To₂ , if this is positive then To₂ is the currently better alternative.

 

51) Criterion of the present value calculated them on the investment total:

Currency the present value them of the alternatives To₁ and To₂ , then the currently better alternative turns out to be that one with a present value them greater.

 

52) Criterion of the TIR calculated on the investment increases them:

Currency the TIR of the cash flow difference of the flows To₁ and₂ , if this is greater of the MARR then To₂ is the currently better alternative.