Credit products. Methods and algorithms of calculation
Credit products
In "Budget-Plan Express" you can easily plan for credit and leasing products of any complexity. For users, there are three types of products that you need to select from the list: Standard, Annuity, and Consumer. Choosing the type of product, the user immediately selects the formula and the standard algorithm by which payments will be calculated. Using additional settings, the user can simulate almost any unique credit product.
When choosing a product type, the user selects the formula and algorithm by which payments will be calculated:
- A "standard" loan product assumes the calculation of differentiated payments using simple and complex percent formulas.
- An "annuity" loan product is equal in amount (usually monthly) payments, which include the amount of accrued percent for a loan and the amount of the principal debt. Two formulas are used to calculate annuities - using simple and compound percentages.
- A "consumer" loan product, like "Standard", is calculated using standard simple and complex percent formulas. However, the loan is paid in equal installments - annuities, which are calculated by simply dividing the amount of all payments (debt and percent) by the number of payments.
- Standard
"Standard" loan product involves the calculation of differentiated payments by simple and compound percent formulas. Differential payment - when the principal amount of a loan is paid in equal installments, and the accrued percent with each subsequent period decreases, the total amount of payment decreases accordingly. The peculiarity of the calculation algorithm is that percent money is accrued depending on the balance of the debt.
- Annuity
Annuity, in the broadest sense – cash flow with equal intervals and an equal cash inflow.
Here annuity payment is equal to the sum of the (usually monthly) payment on the loan, which includes accrued percent on loans and principal amount. In "Budget–Plan Express" uses two formulas to calculate annuities is with the use of simple and complex percent.
1. Annuity with application of the formula of simple percents.
The formula for calculating interest-bearing money (when simple percents are used) is as follows:
A_{1}(1+(n-1)p)+A_{1}(1+(n-2)p)+...A_{1} = Z(1+np), here find the annuity:
A_{1} = Z(1+np)2 / (2+(n-1)p)n,
Where:
A_{1} – annuity payment using simple percent,
Z – loan amount,
n – coefficient years,
p – percent rate coefficient.
2. Annuity with application of the formula of complex percents.
By analogy of deducing the annuity formula using simple percentages, we can write an equation for complex percentages:
A_{2}(1+p)^{(n-1)}+A_{2}(1+p)^{(n-2)}+...A_{2} = Z(1+p)^{(n)}, here find the annuity:
A_{2} = Zp(1+p)^{(n)} / [(1+p)^{(n)} – 1],
Another option (equivalent transformation) the same formula:
A_{2} = Zp / [1 – (1+p)^{(-n)}],
Where:
A_{2} – annuity payment using compound percent,
Z – loan amount,
n – coefficient years,
p – percent rate coefficient.
This formula, using complex percent, is the most common for calculating annuities.
- Consumer
"Consumer" credit, like "Standard", is calculated using standard simple and complex percent formulas. However, the loan is paid in equal installments - annuities , which are calculated by simply dividing the sum of all payments (debt and percent) by the number of payments:
A_{1} = Z ( 1+ pn ) / m - the formula for easy percent.
Where:
A_{1} – annuity payment using simple percent;
m – number of annuities (payments).
A_{2} = Z ( 1+ p )^{n} / m - the formula for complex percent.
Where:
A_{2} – annuity payment with complex percent;
m – number of annuities (payments).
Methods and algorithms of calculation
1. Options for calculating loan products
In the program, all payments are discounted at the end of periods and the payments are called postinumero.
The maximum term of calculating loans is 10 years (120 months).
Note, as the timeline in Budget Plan Express 3 waaga (36 months), all payments, after 36 months, refer to the
future.
In "General settings" to specify General options:
- Calculation step (in months, days)
- Annual cycle accounting method (ACT / ACT, ACT / 360, 360/360);
- Limit percentage
- Estimated percent (simple, complex)
- Calculation currency.
Choosing a formula and calculation conditions, you can simulate almost any calculation. To terms of calculation, in addition to general settings, include:
- Periodicity of payments;
- Deferred debt;
- Deferred percent;
- Accounting for an arithmetic or geometric progression
- Accounting for other one-time payments
- Accounting for other periodic payments;
- Bid adjustment.
For custom calculations you can use the tab "
table of payments" where you can specify the payments schedule.
2. Payments calculated in the currency
All payments are displayed in the "table of payments" in the currency to which they relate. At the time of payment, in the "table of payments" are calculated expense (income) related to currency exchange in system (basic) currency. At the same time, all calculations in the financial plan represented in the system (primary) currency. In the statement of profit and loss exchange rate differences reflected in the line (16): "other non-operating expenses (income)" and not included in "debt servicing Costs".
When calculating the credit, for example, in dollars, in the "financial plan" they will be recalculated in rubles at the forecasted rate.
3. Progressive payment of the debt
Progressive payouts are only used for the "standard" loan product where the percent money is repaid depending on the balance owed.
1. Payments varying in arithmetic progression:
Z = [2B_{1} + d (n-1)] n / 2, hence the first payment of the debt:
B_{1} = Z / n - d(n-1) / 2,
Where:
Z – amount of debt,
B_{1} – the first payment of the debt,
d – the difference of the arithmetic progression (amount).
2. Payments, and variable geometric progression:
Z = B_{1} [q^{n} - 1] / [q - 1], hence the first payment of the debt:
B_{1} = Z [q - 1] / [q^{n} - 1],
Where:
Z – amount of debt,
B_{1} – the first payment of a debt,
q –denominator of geometric progression (percentage).
4. Methods for determining the number of days
In world practice there are several ways of determining the term of loan return t (in years) for loans issued to
period calculated in days. In each of these ways time
the repayment of the loan t (in years) is calculated by the formula:
t = s / g,
where s and g are defined depending on the calculation method:
1. "English" way or ACT / ACT .
The number of s is equal to the exact number of days of a loan minus one day (day
of issue and date of repayment of the loan is considered one day), the number of g is equal to the exact number of days in year (365 or 366). This method
is called English and is often referred to as a way 365/365
or ACT/ACT.
2. "French" way or ACT / 360 .
The number of s is equal to the exact number of days of a loan minus one day (day
of issue and date of repayment of the loan is considered one day), the number
g is equal to 360 (a year has 12 months of 30 days). This method
called the French and is often referred to as a way
365/360 or ACT/360.
3. "German" way or 360/360 .
The number g is 360 (in the year 12 months to 30 days), the number s
consists of a full number of months (30 days each) plus an accurate
number of days in the remaining incomplete month minus one day
(the day of issue and the day of repayment of the loan are considered one day).
This method is called German and is often referred to as
method 360/360.
In financial practice, to determine the exact number of loan days t, use special date tables.
In the "Budget-Plan Express" algorithm for determining the exact number of days is already contained in the calculations. To use this algorithm, you need to specify the calculation step in days (the "settings" tab).
5. Method of calculating the maximum percent at the refinancing rate
The percentage limits is the marginal value of percent deductions, including percent and sum differences on obligations. Is calculated based on refinancing rate: refinancing rate multiplied by a factor.
Depends on the tax law (of any country) in a particular case. In some tax jurisdictions, the ratio may depend on the loan currency. For example, marginal rate in rubles = refinancing rate * 1.8 or ceiling rate currency = refinancing rate * 0.8 or greater.
6. Calculation of simple and complex percent based on the percent rate
The calculation of the credit payment scheme simple percent is calculated by the formula:
K_{(t)} = Z (1 + pt),
Where:
K_{(t)} – payments for the period t.
t – the ratio of the number of years (t = the number of days / 360 = number of days / 365. If the calculation step month, t = the number of months / 12).
p – the percent rate.
Formula of complex percent is from the same formula:
K_{1} = Z ( 1+ p )
K_{2} = Z ( 1+ p )( 1+ p ) = Z( 1+ p )^{2}...
Thus, the calculation of loan payments according to the scheme
complex percent is calculated by the formula: