Interest: The interest on a loan is the time value of money (the cost of the non-availability in time of that money)
C = Capital M = Amount I = Interest VP = Present Value VF = Future Value
financial-math-conceptsA capital deposited on day 0 generates interest over time, the sum of these values results in the amount.
VP + I = VF M = C + I Present Value = Present Value Nominal Value = Future Value
Effective Interest Rate:
(i) It is the interest that a monetary unit generates during a unit of time
Discount Effective Rate
(d) It is the discount made for advancing a monetary unit one unit of time
Simple interest
Generates interest in any unit of time whatever it is
(i) Simple interest rate
Compound interest
It generates interest for a unit of time, it is the value of the placement at the beginning of each unit of time that is being analyzed that generates interest, it is in this way that the capitalization of interest occurs. At the end of each period, interest is part of the capital.
Simple Commercial Discount
The effective discount rate is applied for each unit of time (whatever it may be) over time "N"
Composite Trade Discount
The effective discount rate is applied to the final value of each unit of time that you want to go back.
Simple Rational Discount
The effective discount rate is applied for each unit of time, regardless of the value at that moment.
Rational Compound Discount
The effective rate is applied to the value of the beginning of the time unit that you want to go back.
Rate Equivalence
It is said that two rates are equivalent when the same present values after the same amount of time are transformed into equal future values where they have two characteristics 1) between the different rates involved in a single calculation formula 2) between the rates corresponding to different formulas calculation of interest or discount.
At equal present values with equal times the rates are equal
Types of Fees
Simple Interest Rate
It is the one that at the end of a period is applied only to the initial capital, constant capital during the time of the financial operation, as well as the interest accrued at the end of each period (accrued is what happens in each period)
Compound Interest Rate
It is the interest rate that at the end of each period is applied both to the previous capital and to the interest accrued at the end of that period. This is equivalent to saying that it is the operation where interest generates interest, through the capitalization system.
Effective Rate
It is the interest rate that is actually applied in the compounding period on a principal to calculate the interest.
The effective interest rate is identified because only the numerical part appears followed by the period of capitalization or interest settlement.
For example, an interest rate of 3% is said, monthly 9%, quarterly 15%, semi-annual or 32%, annually but they are not equivalent
Nominal Interest Rate
It is the interest rate that, expressed annually, capitalizes several times a year, for that reason the nominal rate does not reflect the reality in terms of interest accrued annually and hence its name.
Unlike the effective rate that does indicate the true interest accrued by a capital at the end of the respective period.
However, in most financial operations the nominal rate is used to express the interest rate that must be paid or charged in that operation. This implies that to perform the financial operations calculations, the first thing to do is convert this nominal rate to the effective rate in each capitalization period because, as already noted, we must only use the effective rate per period.
Inflation Impact on Rates
Inflation: It is the sustained increase in prices
The effective rate of inflation is the growth suffered by the price of a certain basket of goods and services expressed as per 1 during a unit of time.
Real Interest Rate
There are two parts: the expected inflation rate (h) and the rate that rewards the sacrifice of not having the money for a certain period of time.
(i) Effective interest rate at which the loan is made
(h) Expected effective inflation
rate (r) Real effective rate
Income
It is a set of benefits with different maturities, each of which are called terms or rent quota. We can also define it as a succession of payments or collections maturing at equidistant times or regular intervals, the period as an interval of time that mediates between two consecutive payments.
The duration of a rental is the number or amount of terms or installments.
• Certain income _ All elements are known in advance
• Random or contingent rents _ May vary according to circumstances that cannot be controlled in advance
At each instant in the timeline, a Real No. is assigned called (t)
For the income calculations, business days and business year are used 30 days a month and 360 days a year.
Value of a Rent
It is a monetary figure of relative magnitude that acquires its true meaning when it is referred to a certain instant of time. For example, saying $ 100 does not make sense if it is not specified when that figure may be available, today, tomorrow, or in a year.
Two figures expressed at different times are heterogeneous in financial terms, not comparable to themselves unless a functional rule is taken that allows defining an equivalence relation in such a way as to homogenize those figures.
The rule is none other than the compound interest formula
The value of an income will be a series of benefits, a number of monetary units in an instant of time (t) equidistant in financial terms to the set of payments that make up that income.
Constant Income
Rent at time t with interest i is the sum of all the installments from 1 to n carried at time t
It is the sum of k = 1 to k = n of Ck (t, i)
Investment
It is a process that consists of the application of funds generally associated with obtaining assets in order to obtain a benefit, not necessarily economic, that compensates the sacrifice imposed by the availability of the invested funds.
The presence of funds is an essential requirement, a time and a flow of payments or funds that are located at different instants of time. They can be bonds, machinery, renovation and replacement, investment for expansion, etc.
It can be public or private, legal or physical.
What is sought is to be able to value different investments.
NPV = Net present value (net = income - costs = net income)
NPV = Net Present Value
IRR = Rate of Return or Internal Rate of Return
NPV = Average Net Present Value
TCC = capital cost rate = i
NPV Net Present Value
We will call the NPV of the investment the amount of money equivalent in financial terms to the set of payments or collections that represent the set of investment funds. (equivalents for the capital collection rate) said NPV is calculated at the time of the initial disbursement or zero point.
IRR Internal Rate of Return
At the discretion of the VPN option to invest will be decided according to the present value of revenues minus cash outflows updated rate Capital costs
The method of calculating that rate reproduce funds invested and then analyze if that rate is or not enough to consider the investment convenient
The rate of return or IRR of an investment is called the rate at which the NPV of an investment becomes 0, the rate is defined as effective in the period in which the net income is defined, and it is convenient to invest to the extent that the The rates offered by the investment (R) exceed the TCC (i) both defined in the same unit of time.
It is the rate at which the present value of the receipts is equated with the present value of the payments.
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