Interest rate scale

The interest scale is used when calculating the interest for accounts with ongoing credits and debits and interest rate changes. Bank accounts such as current accounts, giro accounts, overnight money, savings accounts, etc., but also, for example, financial accounts and rental accounts are settled in this way. On some accounts, e.g. B. Current account credit with the bank, there is the possibility that the balance changes from debit to credit and vice versa, that is, that the account holder is debtor or creditor of the bank depending on the account balance . Usually different interest rates are used for debit and credit . In the case of a current account loan, for example, the interest on the loan is higher than on credit.

Calculation of interest

With the interest scale, the interest is always calculated up to a change in the account balance (deposit or withdrawal) or a change in the interest rate and accumulated (staggered) until the next capitalization . At the time of capitalization, the accumulated interest is then added to the capital (capitalized).

Day calculation : The calculation of the days depends on the agreement. Two methods are common: With the calendar method, the days are calculated exactly according to the calendar. With the commercial method, however, the months are generally calculated with 30 days and the years with 360 days. In general, the first day is not counted, but the last day is.

Capitalization: The point in time at which the accrued interest is added to the capital (capitalization) is also different. In the case of the savings book, the interest is usually added annually to the capital, in the case of overdrafts it is trimestral, i.e. every three months. Other capitalization dates are also possible.

Calculating the interest: To calculate the interest for a certain period of time, the number of days in relation to the anniversaries must be taken into account in the interest formula. Depending on the calculation method, the anniversaries are 360 or 365 or 366 for a leap year.

{\ displaystyle Z = {\ frac {k \ cdot p} {100}} \ cdot {\ frac {T} {365}}}

,

where stands for interest, for capital, for the rate of interest and for the calendar number of days per year. ${\ displaystyle Z}$ ${\ displaystyle k}$ ${\ displaystyle p}$ ${\ displaystyle T}$

Example:

Period: May 2, 2007 to June 20, 2007 Interest rate: 5%, that is , ${\ displaystyle p = 5}$

Capital: 1000

Daily calculation: according to the calendar

Days per year: by calendar

{\ displaystyle Z = {\ frac {1000 \ times 5 \ times 49} {100 \ times 365}} = 6 {,} 71}

Example of an interest rate scale

To settle the interest of an account with ongoing deposits and withdrawals, the movements are recorded according to the following scheme:

		Movements		balance
date	description	Should	To have	Should	To have
01/01/2007	transfer		2000		2000
01/20/2007	Deposit		150		2150
01/25/2007	Withdrawal	2700		550
01/28/2007	Deposit		450	100
03/31/2007	graduation

Note: The terms debit and credit are usually chosen from the point of view of the bank, so that debit means a credit or minus from the perspective of the account holder and credit means a credit or plus. If the account is private or business, the terms are reversed, which is correct from an accounting point of view.

The table is supplemented by the columns days and interest figures for billing purposes . It is also important to note that a higher interest rate is usually charged for borrowing money (credit) than is paid for making money (debit) available. The banks cite the default risk and administrative costs as reasons.

The interest figures: To simplify the settlement, part of the above formula is extracted.

From the interest formula:

{\ displaystyle {\ frac {K \ cdot p \ cdot T} {100 \ cdot 365}}}

becomes the interest rate formula

{\ displaystyle {\ frac {K \ cdot T} {100}}}

extracted. At the end the interest numbers are added up and with the remaining part of the formula

{\ displaystyle {\ frac {p} {365}}}

multiplied. With that the interest is calculated.

While the manual staggering of the interest, as it was common before the days of calculators and computers, the workload through the interest figures was enormous, it no longer plays a role today.

Calculation: the borrowing rate is 2%, the credit rate is 5%

		Movements		balance			Interest numbers
date	description	Should	To have	Should	To have	Days	Should	To have
01/01/2007	transfer		2000		2000	19th		380
01/20/2007	Deposit		150		2150	5		107
01/25/2007	Withdrawal	2700		550		3	16
01/28/2007	Deposit		450	100		62	62
03/31/2007	graduation					Days	78	487

The interest figures multiplied by gives: ${\ displaystyle {\ frac {p} {365}}}$

{\ displaystyle {\ text {Debit interest}} = 78 \ cdot {\ frac {2} {365}} \ approx 0 {,} 43}

{\ displaystyle {\ text {Credit interest}} = 487 \ cdot {\ frac {5} {365}} \ approx 6 {,} 67}

{\ displaystyle {\ text {difference}} = 6 {,} 67-0 {,} 43 = 6 {,} 24}

So: As of March 31, 2007, credit interest of 6.24 will accrue. With quarterly account closing, this interest would be posted as a credit movement and added to the capital.

literature

W. Grundmann, B. Luderer: Collection of formulas for financial mathematics, actuarial mathematics, securities analysis. 2nd edition, BG Teubner Verlag, Wiesbaden 2003, ISBN 3-519-10290-0 .

Web links

Interest rate scale

contents

Calculation of interest

Example of an interest rate scale

See also

literature

Web links