Monthly Fixed Payment (MFP) - one of kinds of payments in the mortgage. FP - uniform unchangeable payment on all term of crediting. A FP are subdivided on Relative (RFP) and Absolute (AFP).
RFP are expressed in percentage or shares from the sum of the credit
AFP in monetary units (roubles, dollars...).
AFP is equal to product of a RFP on the Sum of the Credit (SC)
AFP = RFP * CS
Basic data, designation and reduction:
SC = 1 - sum of the credit
n - quantity (amount) of a FP - equal payments, of Interest Periods (InP)
p - the Interest Rate (IR) (in shares) for 1 InP (If p = 1%, a share = 0,01)
k - number of payment
Dk - duty after k-payment
Dn = 0, since the borrower completely has settled up under the credit
a - size of a RFP
auxiliary factor - q is applicable
q = 1 + p, where
p - IR (in shares) behind a InP
With each subsequent FP the rest of the debt, on which percent (interest) is charged up to zero the ambassador decreases the latter of a FP
Dk = Dk-1 + Dk-1 * p - a = Dk-1 * (1+p) - a = Dk-1 * q - a
SC = 1 > D1 > D2 >... > Dk-1 > Dk > Dk+1... > Dn-1 > Dn = 0
SC = 1
D1 = SC + CS * p - a = SC * (1+p) - a = CS * q - a = 1 * q - a = q - a
SC = 1 > D1 = SC + CS * p - a = 1 + p - a
i.e.
1 > 1 + p - a
0 > p - a
a > p = (q-1)
since it is obvious, if a RFP = a less than p or a = p, the borrower never will settle up with bank
D2 = D1 + D1 * p - a = D1 * (1+p) - a = D1 * q - a = (q - a) * q - a = q2 - a * q - a
D3= D2 * q - a = (q2 - a * q - a) *q - a = q3 - a * q2 - a * q - a = q3 - a * (q2 + q + 1)
-
Dk = Dk-1 * q - a = qk - a * (qk-1 + qk-2 +...+ q + 1)
-
Dn = Dn-1 * q - a = qn - a * (qn-1 + qn-2 +... + q + 1) = 0
i.e.
qn = a * (qn-1 + qn-2 +... + q + 1)
The Right part of the equation - sum of the n-members of a geometrical progression.
We shall multiply and divide it on (q - 1)
qn = a * (qn-1 + qn-2 +... + q + 1) * (q - 1) / (q -1)
qn = a * (qn - qn-1 + qn-1 - qn-2 + qn-2...- q + q - 1) / (q - 1)
qn = a * (qn - 1) / (q - 1)
Whence
a = (q - 1) *qn / (qn - 1) = (q - 1) * (qn - 1 + 1) / (qn - 1) = (q - 1) * [1 + 1 / (qn - 1)] = (q - 1) + (q - 1) / (qn - 1]
or
a = (q - 1) * qn / (qn - 1)
If we shall divide numerator and denominator on qn,
a = [(q - 1)*qn / qn] / [(qn - 1) / qn] = (q - 1) / (1 - 1/qn) = (q - 1) / (1 - q-n)
Knowing, that q = 1 + p or p = q -1, we receive the following Formulas Account of a RFP
| 1 | (q - 1) + (q - 1) / (qn - 1] | 1a | p + p / [(1 + p)n - 1] |
|---|---|---|---|
| 2 | (q - 1) / (1 - 1/qn) | 2a | p / [1 - 1 / (1 + p)n] |
| 3 | (q - 1) / (1 - q-n) | 3a | p / [1 - (1 + p)-n] |
RFP both AFP - relative and absolute FP
SC - sum of the credit
p - IR (in shares) behind a InP (if p = 1,2 %, a share = 0,012)
n - quantity (amount) of a FP or InP
RFP both AFP - relative and absolute FP
SC - sum of the credit
p - IR (in shares) for one year (if p = 12 %, a share = 0,12)
p/12 - IR for one month - InP
n - quantity (amount) of a FP or InP
1. SCs - 1 mln rbls; a IR - 15 %/years = 1,25 %/months = 0,0125; term - 30 years - 360 FPs or InP
RFP = a = p + p / [(1 + p)n - 1] = 0,0125 + 0,0125 / [(1 + 0,0125)360 - 1]
= 0,012644 = 1,264%/months from a SC
AFP = CS * RFP = 1000000 * 0,012644 =12644 rbls = 12,64 TRs/months
Sum of a RFP = n * RFP = 360 * 1,264 % = 455% from a SC
2. The same credit in Constant Roubles (CR)
by a Rouble IR - 15 %/years at the Disputable Inflationary Forecast - 12 %/years correspond (meets)
to a IR in a CR - 2,678 %/years ( 1,15/1,12 = 1,02679; = 2,678%)
SC - 1 mln CRs; a IR in a CR - 2,678 %/years = 0,223 %/months = 0,00223; term - 30 years
- 360 FPs or InP
RFP = a = p + p / [(1 + p)n - 1] = 0,00223 + 0,00223 / [(1 + 0,00223)360 - 1]
= 0,004045 = 0,4045%/months from a SC
AFP = CS * RFP = 1000000 * 0,004045 = 4045 CRs = 4,05 TCR/months
Sum of a RFP = n * RFP = 360 * 0,4045% = 145,6% from a SC
The application of a CR will allow to the borrowers to take in times the greater credit (In the indicated example in 3,125 times it is more), i.e. for many years earlier to decide housing problem. The borrower begins to pay, instead of another's employed rising in price housing accommodation. To pay it is necessary at a growing rate of a CR, but the game costs (stands) of candles. At advance settlement it is possible to settle up much faster than for 30 years.
The CR decides a problem of the Disputable Inflationary Forecast. The investors receive an opportunity real preservations and augmentation of a buying power of the savings. The borrowers receive more accessible credits. Arrived of banks also will increase, since the trust of the investors will be increased, essentially will increase volumes and quantity (amount) of the placed contributions and given credits.
Important theme. Without tax reform will not be essential growth economy and standard of living, neither new housing accommodation, nor decision of housing problem.
The Parasitic Inflationary Taxes (PIT) "eat" enclosed in production the capitals: constant and turnaround, salary and pension. This theme is more important than the mortgage, since from anything is received anything.
An Example of a PIT for a Working capital (WC)
- Inf - 0 %: the Prices, the Cost Price (CP) and rate of a CR do not vary. The businessman
Somebody on 100 Millions Roubles (mr) has acquired components. They were not necessary, and in one
year he has reseiled them till a CP for the same 100 mrs. Profit or Added Cost (AC) - 0. The taxes - 0.
Losses - PIT - 0. Is possible at necessities to acquire new components.
- Inf - 100 %:The Prices, CP and rate of a CR for one year are doubled. In the beginning of year 100
mCRs = 100 mrs. In one year 100 mCRs = 200 mrs. Somebody reseils furnishing on a new CP, since the prices were
doubled, for 200 mrs, receives imaginary inflationary profit (or imaginary inflationary AC) - 100 mrs, pay
the taxes (from the imaginary profit?!) - 50 % - 50 mrs. He still has 150 mrs or 75 mCRs, on which it is
possible to acquire only 75% of components. Real losses - 25% real buying power of a WC. It also is a PIT for
a WC.
The indicated example of a PIT is equal half of ifference between a new real CP and old, indicated in tax
declarations. I.e. at a zero Inf of a PIT is not present in general, since. The CP does not vary. With growth
of a Inf the burden of a PIT grows also.
The Losses from a PIT somebody will transfer on the salary of the hired workers. If he will cover the business, the workers and their families, in general, will stay without a piece of bread.
From the indicated examples it is visible, that at a zero Inf of a PIT is not present in general. With growth of a Inf the burden of a PIT grows also.
Tax reform
The essence of tax reform - legislative fixing in the tax declaration of the Cost Price in a CR, that will
allow to get rid of a PIT and to make production favourable and fast growing. It:
- New jobs and decrease(reduction) of unemployment
- Essential growth of real wages and pensions
- Additional tax receipts at fast growing economy
- Decrease (reduction) of expenditures on public account on the unemployment benefits
- Etc.
The mortgage begins with comparison of variants. Here 4 comparative tables with percentage by the rates -
0; 1;... 18; 19%/years and with terms of crediting - 5, 10, 15, 20, 25, 27 and 30 years:
1 - Monthly Fixed Payments (MFP)
2 - Factors of Credit Status (FCS). With the help of a FCS it is possible to expect as the much as possible
allowable sums real estates
3 - Sum of a MFP for all term of crediting
4 - Sum of percents (interests) for all term of crediting
