# Interest Rate Calculation

## Continuously and Second-by-second

OANDA pays interest rates on the account balances, and it pays and charges interest rates on the currency pairs currently held in customer positions. Moreover, OANDA calculates interest rates charged and paid continuously, second-by-second. This is in contrast to other financial markets, where interest rate payments are made at daily intervals with the shortest increment of one business day. This document describes how interest rates are charged and paid.

Interest rates vary from currency to currency, and they can change on a daily basis. There are two types of interest rates that come in to play in this context: lending (ask) interest rates apply when OANDA lends you money to buy a currency, and borrowing (bid) interest rates apply when OANDA holds your money. Lending rates are always higher than borrowing rates (e.g., when the bank lends you money, it charges a higher interest rate than it gives you on the money on your accounts).

## Interest Crediting and Debiting

OANDA interest crediting and debiting is performed daily at 4pm EST, and whenever an open trade is closed. Hence, interest on the account balance is credited at 4pm EST each day, with an appropriate entry in the transaction table of each account. Since the account balance is held in USD, the USD borrowing rate is applied. To calculate the account balance interest at 4pm, OANDA analyses the account balance held during each second of the previous 24 hours and pays interest accordingly. For example, if the account balance at 4pm was \$10,000 and it changes to \$12,000 at 10pm the same night and stays at \$12,000 until 4pm the following day, then 6 hours worth of interest is calculated on \$10,000 and 18 hours worth of interest is calculated on \$12,000.

Calculating interest on open trades is more involved. An open trade, say 1000 units of EUR/CHF, involves two currencies: the Euro and the Swiss Franc. If the open trade is long (i.e., you bought Euro and sold Swiss Francs), then you effectively are long (i.e., you hold) 1000 Euro and OANDA pays you the borrowing interest rate on the 1000 EURO for the duration you hold the trade. At the same time, you are short on the equivalent amount of Swiss Francs, so OANDA charges you the lending interest rate on that amount for the duration of the trade. These interest rates are converted to USD before they are credited/charged to your account.

If the open trade is short (i.e., you sold Euro and bought Swiss Francs), then you are short EUR and OANDA charges you lending interest rates for that amount of EUR, and you are long CHF and OANDA pays you borrowing interest rates for the corresponding amount of CHF.

## How Interest is Calculated

The specific algorithm used to calculate the interest on an open trade in XXX/YYY is as follows:

For a long position:
1. calculate the borrowing interest on XXX for the duration in question and convert it to USD
2. calculate the lending interest on YYY for the duration in question and convert it to USD
3. subtract (2) from (1). If negative, then this is the interest you owe --- if positive, then this is what OANDA will pay.

For a short position:
1. calculate the borrowing interest on YYY for the duration in question and convert it to USD
2. calculate the lending interest on XXX for the duration in question and convert it to USD
3. subtract (2) from (1). If negative, then this is the interest you owe — if positive, then this is what OANDA will pay.

OANDA credits or debits interest on the account (with an appropriate transaction) for trade that is open at 4pm, calculated for the time interval starting at 4pm the previous day or the time the trade was made, whichever is later, and ending at 4pm. When a trade is closed, OANDA credits or debits interest on the account for the trade, calculated for the time interval starting at the previous 4pm or the time the trade was opened, whichever is later, and ending at the time the trade is closed.

Let us consider two specific examples.

## Example 1: Buy 1000 units EUR/JPY @ 91.7308 on Monday Jan 1, 2001 at 12:02 a.m.

Assume that the following interest rates apply for Monday Jan 1, 2001:

EUR - 4.76 / 4.81%
JPY - 0.28 / 0.38 %

Note that the borrowing rate is quoted first, followed by the lending rate, and that interest rates are quoted in percentage points per year.

Now assume that the trade is closed at 5:45am later the same day on Jan 1, 2001. The amount of time the trade is held open is 20580 seconds (= 12:01am - 5:45am), or 0.00065214 years (20580 secs / 31557600 secs --- there are 31,557,600 seconds in a year).

For calculating the interest obtained on our EUR position, we use the following formula:

units * lifetime (in years) * EUR borrowing interest rate (%/year) * conversion to USD

If we plug in the appropriate numbers, we obtain:

1000 * 0.00065214 * 4.76% * EUR/USD bid exchange rate
= 1000 * 0.00065214 * 0.0476 * 0.8423
= USD 0.0261

For calculating the interest charged on our JPY position, we first note that we effectively are short 1000 Euros worth of Japanese Yen, which, with the exchange rate of 91.7308 is 91730.8 units of JPY (= 1000 * 91.7308) on which interest is charged. We then use the following formula similar to the one used above:

units * lifetime (in years) * JPY lending interest rate (%/year) * conversion to USD

If we plug in the appropriate numbers, we obtain:

91730.8 * 0.00065214 * 0.38% * JPY/USD ask exchange rate
= 91730.8 * 0.00065214 * 0.0038 * 0.00918
= USD 0.00209

The account will be credited by the difference between the interest to be credited and the interest to be debited:

\$0.0261 - 0.00209 = USD 0.02401

Note that in this case the customer is collecting significantly more money than they are paying, due solely to the discrepancy in interest rates between the base and the quote currencies. In this instance, the base currency (EUR) interest rate is higher than the quote (JPY) interest rate, which is referred to as a "discount" quotation.

If the inverse were true (base currency interest rate lower than the quote currency interest rate), the instrument would be said to be quoted at "premium".

## Example 2: Sell 2000 units GBP/CHF @ 2.5882 on Monday Jan 1, 2001 at 04:02 a.m.

Assume that the following interest rates apply for Monday Jan 1, 2001:

CHF - 3.18 / 3.28 %
GBP - 5.97 / 6.00 %

Note again that the borrowing rate is quoted first, followed by the lending rate, and that interest rates are quoted in percentage points per year.

Assume that this trade is also closed at 5:45am later the same day on Jan 1, 2001. The amount of time the trade is held open is 6180 seconds (= 04:00am - 5:45am), or 0.00019583 years (6180 secs / 31557600 secs)

For calculating the interest obtained on our CHF position, we first calculate the number of CHF units the interest is applied to: 2000 GBP units worth of CHF with the exchange rate of 2.5882 is 2000 * 2.5882 = 5176.4. Then we apply the following formula again:

units * lifetime (in years) * CHF borrowing interest rate (%/year) * conversion to USD

If we plug in the appropriate numbers, we obtain:

5176.4 * 0.00019583 * 3.18% * 0.5606
= USD 0.01807

For calculating the interest charged on our GBP position, we again use the following formula similar to the one used above:

units * lifetime (in years) * GBP lending interest rate (%/year) * conversion to USD

If we plug in the appropriate numbers, we obtain:

2000 * 0.00019583 * 6.00% * 1.4516
= USD 0.03411

The account will be credited by the difference between the interest to be credited and the interest to be debited:

\$ 0.01807 - \$ 0.03411 =  - USD 0.01604

Since the amount is negative, the aggregate interest is charged to the account.