# time2date

Dates from time and frequency

## Description

computes `Dates`

= time2date(___,`Compounding`

,`Basis`

,`EndMonthRule`

)`Dates`

corresponding
to compounded rate quotes between `Settle`

and `TFactors`

using
optional input arguments for `Compounding`

, `Basis`

,
and `EndMonthRule`

. `time2date`

is
the inverse of `date2time`

.

## Examples

### Calculate Dates Using `time2date`

Show that `date2time`

and `time2date`

are the inverse of each other. First compute the time factors using `date2time`

.

Settle = datetime(2002,9,1); Dates = [datetime(2005,8,31) ; datetime(2006,2,28) ; datetime(2006,6,15) ; datetime(2006,12,31)]; Compounding = 2; Basis = 0; EndMonthRule = 1; TFactors = date2time(Settle, Dates, Compounding, Basis,... EndMonthRule)

`TFactors = `*4×1*
5.9945
6.9945
7.5738
8.6576

Now use the calculated `TFactors`

in `time2date`

and compare the calculated dates with the original set.

Dates_calc = time2date(Settle, TFactors, Compounding, Basis,... EndMonthRule)

`Dates_calc = `*4x1 datetime*
31-Aug-2005
28-Feb-2006
15-Jun-2006
31-Dec-2006

## Input Arguments

`Settle`

— Settlement date

datetime scalar | string scalar | date character vector

Settlement date, specified as a scalar datetime, string, or date character vector.

To support existing code, `time2date`

also
accepts serial date numbers as inputs, but they are not recommended.

**Data Types: **`char`

| `string`

| `datetime`

`TFactors`

— Time factors

vector

Time factors, corresponding to the compounding value, specified
as a vector. `TFactors`

must be equal to or greater
than zero.

**Data Types: **`double`

`Compounding`

— Rate at which input zero rates are compounded when annualized

`2`

(Semiannual compounding) (default) | scalar with numeric values of `0`

, `1`

, `2`

, `3`

, `4`

, `5`

, `6`

, `12`

, `365`

, `–1`

Rate at which input zero rates are compounded when annualized,
specified as a scalar with numeric values of: `0`

, `1`

, `2`

, `3`

, `4`

, `5`

, `6`

, `12`

, `365`

,
or `–1`

. Allowed values are defined as:

`0`

— Simple interest (no compounding)`1`

— Annual compounding`2`

— Semiannual compounding (default)`3`

— Compounding three times per year`4`

— Quarterly compounding`6`

— Bimonthly compounding`12`

— Monthly compounding`365`

— Daily compounding`-1`

— Continuous compounding

The optional `Compounding`

argument determines
the formula for the discount factors (`Disc`

):

`Compounding`

=`1`

,`2`

,`3`

,`4`

,`6`

,`12`

`Disc = (1 + Z/F)^(-T)`

, where`F`

is the compounding frequency,`Z`

is the zero rate, and`T`

is the time in periodic units, for example,`T = F`

is one year.

`Compounding`

=`365`

`Disc = (1 + Z/F)^(-T)`

, where`F`

is the number of days in the basis year and`T`

is a number of days elapsed computed by basis.

`Compounding`

=`-1`

`Disc = exp(-T*Z)`

, where`T`

is time in years.

`Basis`

— Day-count basis

`0`

(actual/actual) (default) | numeric with value `0`

through `13`

| vector of numerics with values `0`

through `13`

Day-count basis, specified as an integer with a value of `0`

through `13`

or
a `N`

-by-`1`

vector of integers
with values `0`

through `13`

.

0 = actual/actual (default)

1 = 30/360 (SIA)

2 = actual/360

3 = actual/365

4 = 30/360 (BMA)

5 = 30/360 (ISDA)

6 = 30/360 (European)

7 = actual/365 (Japanese)

8 = actual/actual (ICMA)

9 = actual/360 (ICMA)

10 = actual/365 (ICMA)

11 = 30/360E (ICMA)

12 = actual/365 (ISDA)

13 = BUS/252

For more information, see Basis.

**Data Types: **`single`

| `double`

`EndMonthRule`

— End-of-month rule flag for month having 30 or fewer days

`1`

(in effect) (default) | nonnegative integer `[0,1]`

End-of-month rule flag for month having 30 or fewer days, specified
as scalar nonnegative integer [`0`

, `1`

]
or a using a `N`

-by-`1`

vector of
values. This rule applies only when `Maturity`

is
an end-of-month date for a month having 30 or fewer days.

`0`

= Ignore rule, meaning that a payment date is always the same numerical day of the month.`1`

= Set rule on, meaning that a payment date is always the last actual day of the month.

**Data Types: **`logical`

## Output Arguments

## Version History

**Introduced before R2006a**

### R2022b: Serial date numbers not recommended

Although `time2date`

supports serial date numbers,
`datetime`

values are recommended instead. The
`datetime`

data type provides flexible date and time
formats, storage out to nanosecond precision, and properties to account for time
zones and daylight saving time.

To convert serial date numbers or text to `datetime`

values, use the `datetime`

function. For example:

t = datetime(738427.656845093,"ConvertFrom","datenum"); y = year(t)

y = 2021

There are no plans to remove support for serial date number inputs.

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