Deriscope ## The Excel Derivatives Periscope

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Simple_Rate__Compounding

*Compounding* refers to List of possible compounding rules that may be part of the interest rate definition.

Each compounding rule, together with the Frequency entry, dictates how the earned interest amount should be capitalized over time, i.e. added to the notional, thus affecting the interest amount earned subsequently.

Available *Compounding* types:

*Compounded*

The earned interest amount should be capitalized over time according to a mathematical formula described below.

Formally, the interest amount *I* earned during any time period with length *t* is given by the formula *I = N(1+r/f)^(ft) - N*

where:

*N* is the notional at the begining of the accrual period

*r* is the applicable fixed rate

*t* is the length of the accrual period in number of years according to some given DayCount convention.

*f* is the compounding frequency of the applicable fixed rate, e.g. 2 if semiannual.

*Compounded Then Simple*

This is equivalent to *Simple* for accrual periods greater than the compounding period corresponding to the given frequency, but equivalent to *Compounded* for accrual periods less or equal than that.

Formally, the interest amount *I* earned during any time period with length *t* is given by the formula *I = Nrt* if t is greater than 1/f and *I = N(1+r/f)^(ft) - N* if t is less or equal than 1/f.

where:

*N* is the notional at the begining of the accrual period

*r* is the applicable fixed rate

*t* is the length of the accrual period in number of years according to some given DayCount convention.

*f* is the compounding frequency of the applicable fixed rate, e.g. 2 if semiannual.

*Continuous*

The earned interest amount should be capitalized continuously over time.

Formally, the interest amount *I* earned during any time period with length *t* is given by the formula *I = Ne^(rt) - N*

where:

*N* is the notional at the begining of the accrual period

*r* is the applicable fixed rate

*t* is the length of the accrual period in number of years according to some given DayCount convention.

*Simple*

The earned interest amount should never be capitalized, which means the notional remains constant.

Formally, the interest amount *I* earned during any time period with length *t* is given by the formula *I = Nrt*

where:

*N* is the notional, which stays constant

*r* is the applicable fixed rate

*t* is the length of the accrual period in number of years according to some given DayCount convention.

*Simple Then Compounded*

This is equivalent to *Simple* for accrual periods less or equal than the compounding period corresponding to the given frequency, but equivalent to *Compounded* for accrual periods greater than that.

Formally, the interest amount *I* earned during any time period with length *t* is given by the formula *I = Nrt* if t is less or equal than 1/f and *I = N(1+r/f)^(ft) - N* if t is greater than 1/f.

where:

*N* is the notional at the begining of the accrual period

*r* is the applicable fixed rate

*t* is the length of the accrual period in number of years according to some given DayCount convention.

*f* is the compounding frequency of the applicable fixed rate, e.g. 2 if semiannual.