PRICE

Microsoft publishes =PRICE(A2,A3,A4,A5,A6,A7,A8) = $94.63 for a bond settled 2008-02-15, maturing 2017-11-15, 5.75% coupon, 6.5% yield, redemption 100, semiannual, 30/360 basis. DERIVATION from the N>1 formula Microsoft prints as an image: price = redemption/(1+yld/f)^(N-1+DSC/E) + sum over k = 1..N of 100*(rate/f)/(1+yld/f)^(k-1+DSC/E) - 100*(rate/f)*(A/E). Settlement 2008-02-15 sits exactly halfway through the coupon period 2007-11-15 to 2008-05-15, so on basis 0 E = 180, DSC = 90 and A = 90, and N = 20 semiannual coupons run from 2008-05-15 through 2017-11-15. Evaluated as twenty individual discounted cash flows at 50 digits -- not through a closed-form annuity shortcut -- that is 94.63436162132213..., which is $94.63 at the published precision. Day counts come from a clean-room implementation of OpenFormula 1.3 section 4.11.7 (Procedure A for US 30/360, Procedure B for actual days, Procedure C for European 30/360, D/E/F for days-in-year) written for this batch and used by no engine. Microsoft's page was re-read live on 2026-08-31 at https://support.microsoft.com/en-us/excel/functions/price-function (the /en-us/office/<name>-function-<guid> path was returning Microsoft's 'Sorry, the page you're looking for can't be found' body throughout this batch, and the working path serves an 87 KB stub about half the time, so pages were fetched with retries until the payload exceeded 150 KB).

Two published decimals cannot see a discounting exponent that is off by half a period, so the cash-flow derivation is asserted at ten places: 94.6343616213.

When the coupon rate equals the yield AND settlement falls on a coupon date, the discounted cash flows are worth exactly par: 100.0000000000. THE SECOND CONDITION IS NOT OPTIONAL, and this case was rewritten after the derivation caught it: settled mid-period, the same bond does NOT price at 100 -- the documented formula gives 100*(1+yld/f)^(A/E) minus the simple-interest accrued 100*(rate/f)*(A/E), and compound growth over the elapsed part of the period does not equal simple accrual over it. On Microsoft's own example dates (settlement 2008-02-15, exactly half a period in) a coupon-equals-yield bond prices at 99.98700716450788, not 100. Settling on 2008-05-15 makes DSC/E = 1 and A = 0, the accrued term vanishes and the identity becomes exact. It is a structural assertion with no derived constant, and it is sharp: an error in the day-count ratios, the discount exponent or the accrued subtraction breaks it while leaving the headline figure looking plausible.

Microsoft documents: "If frequency is any number other than 1, 2, or 4, PRICE returns the #NUM! error value." OpenFormula 1.3 section 6.12.38 states the same constraint.

Microsoft documents: "If basis < 0 or if basis > 4, PRICE returns the #NUM! error value."

Microsoft documents: "If settlement >= maturity, PRICE returns the #NUM! error value." Equality is the boundary the >= includes.

Microsoft documents: "If redemption <= 0, PRICE returns the #NUM! error value." Note the asymmetry with rate and yld, which are excluded only BELOW zero: a zero-coupon bond is legal, a zero-redemption bond is not.

Microsoft documents: "If settlement or maturity is not a valid date, PRICE returns the #VALUE! error value."

Microsoft publishes =PRICE(A2,A3,A4,A5,A6,A7,A8) = $94.63 for a bond settled 2008-02-15, maturing 2017-11-15, 5.75% coupon, 6.5% yield, redemption 100, semiannual, 30/360 basis. DERIVATION from the N>1 formula Microsoft prints as an image: price = redemption/(1+yld/f)^(N-1+DSC/E) + sum over k = 1..N of 100*(rate/f)/(1+yld/f)^(k-1+DSC/E) - 100*(rate/f)*(A/E). Settlement 2008-02-15 sits exactly halfway through the coupon period 2007-11-15 to 2008-05-15, so on basis 0 E = 180, DSC = 90 and A = 90, and N = 20 semiannual coupons run from 2008-05-15 through 2017-11-15. Evaluated as twenty individual discounted cash flows at 50 digits -- not through a closed-form annuity shortcut -- that is 94.63436162132213..., which is $94.63 at the published precision. Day counts come from a clean-room implementation of OpenFormula 1.3 section 4.11.7 (Procedure A for US 30/360, Procedure B for actual days, Procedure C for European 30/360, D/E/F for days-in-year) written for this batch and used by no engine. Microsoft's page was re-read live on 2026-08-31 at https://support.microsoft.com/en-us/excel/functions/price-function (the /en-us/office/<name>-function-<guid> path was returning Microsoft's 'Sorry, the page you're looking for can't be found' body throughout this batch, and the working path serves an 87 KB stub about half the time, so pages were fetched with retries until the payload exceeded 150 KB).

Two published decimals cannot see a discounting exponent that is off by half a period, so the cash-flow derivation is asserted at ten places: 94.6343616213.

When the coupon rate equals the yield AND settlement falls on a coupon date, the discounted cash flows are worth exactly par: 100.0000000000. THE SECOND CONDITION IS NOT OPTIONAL, and this case was rewritten after the derivation caught it: settled mid-period, the same bond does NOT price at 100 -- the documented formula gives 100*(1+yld/f)^(A/E) minus the simple-interest accrued 100*(rate/f)*(A/E), and compound growth over the elapsed part of the period does not equal simple accrual over it. On Microsoft's own example dates (settlement 2008-02-15, exactly half a period in) a coupon-equals-yield bond prices at 99.98700716450788, not 100. Settling on 2008-05-15 makes DSC/E = 1 and A = 0, the accrued term vanishes and the identity becomes exact. It is a structural assertion with no derived constant, and it is sharp: an error in the day-count ratios, the discount exponent or the accrued subtraction breaks it while leaving the headline figure looking plausible.

Microsoft documents: "If frequency is any number other than 1, 2, or 4, PRICE returns the #NUM! error value." OpenFormula 1.3 section 6.12.38 states the same constraint.

Microsoft documents: "If basis < 0 or if basis > 4, PRICE returns the #NUM! error value."

Microsoft documents: "If settlement >= maturity, PRICE returns the #NUM! error value." Equality is the boundary the >= includes.

Microsoft documents: "If redemption <= 0, PRICE returns the #NUM! error value." Note the asymmetry with rate and yld, which are excluded only BELOW zero: a zero-coupon bond is legal, a zero-redemption bond is not.

Microsoft documents: "If settlement or maturity is not a valid date, PRICE returns the #VALUE! error value."

Microsoft publishes =PRICE(A2,A3,A4,A5,A6,A7,A8) = $94.63 for a bond settled 2008-02-15, maturing 2017-11-15, 5.75% coupon, 6.5% yield, redemption 100, semiannual, 30/360 basis. DERIVATION from the N>1 formula Microsoft prints as an image: price = redemption/(1+yld/f)^(N-1+DSC/E) + sum over k = 1..N of 100*(rate/f)/(1+yld/f)^(k-1+DSC/E) - 100*(rate/f)*(A/E). Settlement 2008-02-15 sits exactly halfway through the coupon period 2007-11-15 to 2008-05-15, so on basis 0 E = 180, DSC = 90 and A = 90, and N = 20 semiannual coupons run from 2008-05-15 through 2017-11-15. Evaluated as twenty individual discounted cash flows at 50 digits -- not through a closed-form annuity shortcut -- that is 94.63436162132213..., which is $94.63 at the published precision. Day counts come from a clean-room implementation of OpenFormula 1.3 section 4.11.7 (Procedure A for US 30/360, Procedure B for actual days, Procedure C for European 30/360, D/E/F for days-in-year) written for this batch and used by no engine. Microsoft's page was re-read live on 2026-08-31 at https://support.microsoft.com/en-us/excel/functions/price-function (the /en-us/office/<name>-function-<guid> path was returning Microsoft's 'Sorry, the page you're looking for can't be found' body throughout this batch, and the working path serves an 87 KB stub about half the time, so pages were fetched with retries until the payload exceeded 150 KB).

Two published decimals cannot see a discounting exponent that is off by half a period, so the cash-flow derivation is asserted at ten places: 94.6343616213.

When the coupon rate equals the yield AND settlement falls on a coupon date, the discounted cash flows are worth exactly par: 100.0000000000. THE SECOND CONDITION IS NOT OPTIONAL, and this case was rewritten after the derivation caught it: settled mid-period, the same bond does NOT price at 100 -- the documented formula gives 100*(1+yld/f)^(A/E) minus the simple-interest accrued 100*(rate/f)*(A/E), and compound growth over the elapsed part of the period does not equal simple accrual over it. On Microsoft's own example dates (settlement 2008-02-15, exactly half a period in) a coupon-equals-yield bond prices at 99.98700716450788, not 100. Settling on 2008-05-15 makes DSC/E = 1 and A = 0, the accrued term vanishes and the identity becomes exact. It is a structural assertion with no derived constant, and it is sharp: an error in the day-count ratios, the discount exponent or the accrued subtraction breaks it while leaving the headline figure looking plausible.

Microsoft documents: "If frequency is any number other than 1, 2, or 4, PRICE returns the #NUM! error value." OpenFormula 1.3 section 6.12.38 states the same constraint.

Microsoft documents: "If basis < 0 or if basis > 4, PRICE returns the #NUM! error value."

Microsoft documents: "If settlement >= maturity, PRICE returns the #NUM! error value." Equality is the boundary the >= includes.

Microsoft documents: "If redemption <= 0, PRICE returns the #NUM! error value." Note the asymmetry with rate and yld, which are excluded only BELOW zero: a zero-coupon bond is legal, a zero-redemption bond is not.

Microsoft documents: "If settlement or maturity is not a valid date, PRICE returns the #VALUE! error value."