DOLLARDE

Converts a fractional number representation of a number into a decimal number.

Syntax:

DOLLARDE(fractionalrep, denominator)

fractionalrep: the fractional representation. Sometimes a security price, for example, might be expressed as 2.03, meaning $2 and 3/16 of a dollar.

denominator: the denominator - for example, 16 in the example above.

DOLLARDE converts the fractional representation to decimal. Despite its name, it returns a number, not a currency. Its inverse is DOLLARFR.

Example:

DOLLARDE(2.03, 16)

returns 2.1875 as a number. 2 + 3/16 equals 2.1875.

Application:

Imagine you have a list of U.S. Treasury bond prices. The prices are given in a fractional format where the integer part is the whole dollar amount and the decimal part represents the numerator of a fraction with a denominator of 32.

Here is a table showing some example bond prices in fractional notation and their converted decimal values using the DOLLARDE function.

	Fractional Price	Fraction Denominator	Formula	Decimal Value
	A	B	C	D
1	100.16	32	DOLLARDE(A1, B1)	100.5
2	105.08	32	DOLLARDE(A2, B2)	105.25
3	98.24	32	DOLLARDE(A3, B3)	98.75
4	110.02	32	DOLLARDE(A4, B4)	110.0625
5	102.32	32	DOLLARDE(A5, B5)	103

Explanation of the Formula

The DOLLARDE function has two main arguments:

fractional_dollar: This is the value in fractional notation you want to convert. In the table above, this is the value in Column A. The integer part is the whole number, and the part after the decimal point is the numerator of the fraction.
fraction: This is the denominator of the fraction. For U.S. Treasury bonds, this is commonly 32. This tells the function that the "decimal" part of the number is actually a numerator that needs to be divided by 32.

How it works for the first row:

DOLLARDE(100.16, 32)
The function takes the whole number part (100) and adds the fractional part.
The fractional part is calculated by taking the "decimal" portion (16) and dividing it by the denominator (32).
The calculation is: $100 + \frac{16}{32} = 100 + 0.5 = 100.5$

By using the DOLLARDE function, you can efficiently convert a whole column of fractional prices into a decimal format, which is essential for further financial analysis, such as calculating yield or comparing different bond prices.