Apple Numbers PRICEMAT Function: Maturity-Interest Prices and Accrued Interest

PRICEMAT(settle, maturity, issue, annual-rate, annual-yield, days-basis)

Apple explicitly requires issue < settle < maturity, and both rate arguments must be positive. Enter rates as decimals or percentages. There is no frequency or redemption argument: this is not a periodic-coupon PRICE calculation. Apple’s example can be reconstructed with a maturity payment based on principal 100 plus issue-to-maturity interest, followed by subtraction of issue-to-settlement accrued interest.

Use date-valued cells or DATE(year,month,day) rather than ambiguous text such as 1/2/2026. Settlement is the trade’s settlement date, which need not be its trade date. Apple requires maturity to be later than settlement.

The optional final argument selects:

Basis 0 and basis 4 have different month-end rules. Agreement on the ordinary dates below does not make them interchangeable. The actual-day controls count elapsed calendar days; they do not add an extra day for including both endpoints. These examples do not establish every February-end adjustment or the treatment of a multi-year actual/actual interval.

Enter these values:

Enter =PRICEMAT(A2,B2,C2,D2,E2,F2) in G2. The full formula is:

=PRICEMAT(DATE(2026,4,15),DATE(2026,7,15),DATE(2026,1,15),6%,8%,0)

For these ordinary 30/360 dates, issue to maturity is 180 days, issue to settlement is 90 days, and settlement to maturity is 90 days. Independent reconstruction proceeds in this order:

1. Maturity cash per 100: 100+100*0.06*180/360 = 103.
2. Discount that cash to settlement: 103/(1+0.08*90/360) = 100.9803921569.
3. Accrued interest at settlement: 100*0.06*90/360 = 1.5.
4. Subtract accrued interest: 99.4803921569.

The final figure is the clean-price quote in this reconstruction. The intermediate value including accrued interest is a different amount. Do not subtract accrued interest twice.

Let r be annual-rate, y annual-yield, T issue-to-maturity year fraction, A issue-to-settlement year fraction and D settlement-to-maturity year fraction. For the validated ordinary-date models:

price = (100 + 100*r*T)/(1 + y*D) - 100*r*A

The actual-day controls below use a common fixed annual denominator. This notation does not establish a universal multi-year actual/actual algorithm from Apple’s brief basis descriptions.

For the same 2026 dates, actual issue-to-maturity days are 181, issue-to-settlement 90, and settlement-to-maturity 91. Basis 2 divides each by 360, giving 99.4747331736. Basis 3 divides each by 365, giving 99.4821897202.

Basis 4 and omitted basis both give 99.4803921569 for these ordinary dates. Keeping basis 0 and changing only yield to 4% gives 100.4801980198; yield 10% gives 98.9878048780. The maturity payment and accrued interest remain unchanged in these yield scenarios; only the discount denominator changes.

Apple uses issue December 14, 2008, settlement May 1, 2009, maturity June 30, 2015, stated rate 6.5%, yield 5.25% and basis 0. The reconstructed 30/360 counts are 2356 issue-to-maturity, 137 issue-to-settlement and 2219 settlement-to-maturity.

=PRICEMAT(DATE(2009,5,1),DATE(2015,6,30),DATE(2008,12,14),0.065,0.0525,0)

Calculating (100+100*0.065*2356/360)/(1+0.0525*2219/360)-100*0.065*137/360 gives 105.216355782734, reproducing Apple’s published value. This separate reconstruction supports the accrued-interest treatment instead of borrowing an unstated convention from another product.

For face amount 25000, the first example’s clean cost is approximately 24870.0980392. Accrued interest is 1.5/100*25000 = 375. Their sum is 25245.0980392, before fees or other contractual adjustments. The modeled maturity payment is 103/100*25000 = 25750.

A currency-formatted result depends on language and region settings; it does not change the per-100 unit or automatically scale it to face value. Preserve the quote and scaling calculation separately.

Do not swap issue and settlement, use interest-only cash as principal, or feed a coupon frequency into the basis slot. Zero rates are outside Apple’s documented positive-rate requirements even if a mathematical expression could be evaluated. Exact error tokens, text coercion and untested date boundaries are not established here. No iterative solver, payment schedule or cross-application equivalence is claimed.

The official Apple PRICEMAT reference was checked on October 18, 2026 in Formulas and Functions Help 15.4, within the Numbers 15.4 for Mac documentation context. The worked values in this guide are independent calculations; Apple’s published example is identified separately. No Numbers session or other spreadsheet calculation engine was executed. Cell-reference walkthroughs are instructions, not recorded application tests.

The first release introducing this function is unknown from the checked evidence. The current reference documents it; it does not label it deprecated or retired. Shared iWork documentation does not independently verify every platform, older release or import/export path.

• ACCRINTM
• YIELDMAT
• PRICE