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Finance

 AccruedAmount
 calculate the accrued amount of a bond

 Calling Sequence AccruedAmount(bond, date)

Parameters

 bond - fixed- or floating-rate bond data structure; bond date - a string containing a date specification in a format recognized by ParseDate or a Date data structure; evaluation date

Description

 • The AccruedAmount command computes the interest that is due on a bond since the last interest payment was made. Accrued interest is added to the contract price of a bond transaction.
 • The parameter bond is a fixed coupon bond or floating rate bond.
 • The (optional) parameter date is the evaluation date. By default the global evaluation date is used. It can be specified in any of the standard date formats supported by the package.
 • Note that the value returned by the AccruedAmount command depends on the day count and day rolling conventions used by bond.

Examples

 > $\mathrm{with}\left(\mathrm{Finance}\right):$
 > $\mathrm{SetEvaluationDate}\left("March 15, 2005"\right):$
 > $\mathrm{EvaluationDate}\left(\right)$
 ${"March 15, 2005"}$ (1)
 > $\mathrm{Settings}\left(\left[\mathrm{compounding}=\mathrm{Continuous},\mathrm{settlementdays}=0,\mathrm{businessdayconvention}=\mathrm{Unadjusted}\right]\right)$
 $\left[{\mathrm{compounding}}{=}{\mathrm{Continuous}}{,}{\mathrm{settlementdays}}{=}{0}{,}{\mathrm{businessdayconvention}}{=}{\mathrm{Unadjusted}}\right]$ (2)

Consider a 3-year bond with face value of 100 that pays a fixed coupon of 3 percent issued on March 15, 2005.

 > $\mathrm{Principal}≔100:$
 > $\mathrm{Coupon}≔0.03:$
 > $\mathrm{B1}≔\mathrm{FixedCouponBond}\left(\mathrm{Principal},3,\mathrm{Years},\mathrm{Coupon},\mathrm{issuedate}="March 15, 2005",\mathrm{daycounter}=\mathrm{Thirty360European}\right):$

Here is the same bond but using the ISDA convention.

 > $\mathrm{B2}≔\mathrm{FixedCouponBond}\left(\mathrm{Principal},3,\mathrm{Years},\mathrm{Coupon},\mathrm{issuedate}="March 15, 2005",\mathrm{daycounter}=\mathrm{ISDA}\right):$

Here is the interest accrued before the first coupon payment.

 > $\mathrm{AccruedAmount}\left(\mathrm{B1},"March 14, 2006"\right)$
 ${2.991666667}$ (3)
 > $\mathrm{AccruedAmount}\left(\mathrm{B2},"March 14, 2006"\right)$
 ${2.991780822}$ (4)

Compare this to

 > $\mathrm{Principal}\mathrm{Coupon}\mathrm{YearFraction}\left("March 15, 2005","March 14, 2006",\mathrm{Thirty360European}\right)$
 ${2.991666667}$ (5)
 > $\mathrm{Principal}\mathrm{Coupon}\mathrm{YearFraction}\left("March 15, 2005","March 14, 2006",\mathrm{ISDA}\right)$
 ${2.991780822}$ (6)

This shows the interest accrued right after the first coupon payment.

 > $\mathrm{AccruedAmount}\left(\mathrm{B1},"March 15, 2006"\right)$
 ${0.}$ (7)
 > $\mathrm{AccruedAmount}\left(\mathrm{B2},"March 15, 2006"\right)$
 ${0.}$ (8)

Here is the interest accrued two months after the first coupon payment.

 > $\mathrm{AccruedAmount}\left(\mathrm{B1},"May 16, 2006"\right)$
 ${0.5083333333}$ (9)
 > $\mathrm{AccruedAmount}\left(\mathrm{B2},"May 16, 2006"\right)$
 ${0.5095890411}$ (10)

Compare accrued interest and the difference between the clean price and the dirty price of a bond.

 > $\mathrm{SetEvaluationDate}\left("March 14, 2006"\right):$
 > $\mathrm{EvaluationDate}\left(\right)$
 ${"March 14, 2006"}$ (11)
 > $\mathrm{CleanPrice}\left(\mathrm{B1},0.05\right)$
 ${96.04651941}$ (12)
 > $\mathrm{DirtyPrice}\left(\mathrm{B1},0.05\right)$
 ${99.03818607}$ (13)
 > $\mathrm{CleanPrice}\left(\mathrm{B1},0.05\right)+\mathrm{AccruedAmount}\left(\mathrm{B1}\right)=\mathrm{DirtyPrice}\left(\mathrm{B1},0.05\right)$
 ${99.03818608}{=}{99.03818607}$ (14)
 > $\mathrm{CleanPrice}\left(\mathrm{B2},0.05\right)+\mathrm{AccruedAmount}\left(\mathrm{B2}\right)=\mathrm{DirtyPrice}\left(\mathrm{B2},0.05\right)$
 ${99.03412275}{=}{99.03412275}$ (15)
 > $\mathrm{SetEvaluationDate}\left("March 15, 2006"\right):$
 > $\mathrm{EvaluationDate}\left(\right)$
 ${"March 15, 2006"}$ (16)
 > $\mathrm{CleanPrice}\left(\mathrm{B1},0.05\right)$
 ${96.05194233}$ (17)
 > $\mathrm{DirtyPrice}\left(\mathrm{B1},0.05\right)$
 ${96.05194233}$ (18)
 > $\mathrm{CleanPrice}\left(\mathrm{B1},0.05\right)+\mathrm{AccruedAmount}\left(\mathrm{B1}\right)=\mathrm{DirtyPrice}\left(\mathrm{B1},0.05\right)$
 ${96.05194233}{=}{96.05194233}$ (19)
 > $\mathrm{CleanPrice}\left(\mathrm{B2},0.05\right)+\mathrm{AccruedAmount}\left(\mathrm{B2}\right)=\mathrm{DirtyPrice}\left(\mathrm{B2},0.05\right)$
 ${96.04769000}{=}{96.04769000}$ (20)
 > $\mathrm{SetEvaluationDate}\left("March 16, 2006"\right):$
 > $\mathrm{EvaluationDate}\left(\right)$
 ${"March 16, 2006"}$ (21)
 > $\mathrm{CleanPrice}\left(\mathrm{B1},0.05\right)$
 ${96.05695047}$ (22)
 > $\mathrm{DirtyPrice}\left(\mathrm{B1},0.05\right)$
 ${96.06528381}$ (23)
 > $\mathrm{CleanPrice}\left(\mathrm{B1},0.05\right)+\mathrm{AccruedAmount}\left(\mathrm{B1}\right)=\mathrm{DirtyPrice}\left(\mathrm{B1},0.05\right)$
 ${96.06528380}{=}{96.06528381}$ (24)
 > $\mathrm{CleanPrice}\left(\mathrm{B2},0.05\right)+\mathrm{AccruedAmount}\left(\mathrm{B2}\right)=\mathrm{DirtyPrice}\left(\mathrm{B2},0.05\right)$
 ${96.06084812}{=}{96.06084812}$ (25)

Compatibility

 • The Finance[AccruedAmount] command was introduced in Maple 15.