Apple Numbers RECEIVED Function: Maturity Amounts and Discount Arithmetic

RECEIVED(settle, maturity, invest-amount, annual-rate, days-basis)

Apple requires a positive annual-rate and documents invest-amount as nonnegative. Use a consistent currency for the input and result. Unlike per-100 pricing functions, investment is an actual cash amount.

With investment I, rate d and year fraction t, the model matching Apple’s example is:

maturity amount = I / (1 - d*t)

This rearranges I = maturity amount * (1-d*t). Thus the discount is measured from maturity value, not from investment. The examples use positive investment and a positive denominator; untested zero and singular cases are discussed separately.

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.

Set A2 to =DATE(2026,1,15), B2 to =DATE(2026,7,15), C2 to 10000, D2 to 8% and E2 to 0. In F2 enter =RECEIVED(A2,B2,C2,D2,E2).

=RECEIVED(DATE(2026,1,15),DATE(2026,7,15),10000,8%,0)

The ordinary 30/360 fraction is 180/360. First calculate the discount fraction 0.08*0.5 = 0.04; then divide investment by 1-0.04 = 0.96. The independent maturity amount is 10416.6666667, including the original investment. The gain is approximately 416.6666667.

For maturity April 15, 2026, the fraction becomes 90/360 and the result is 10204.0816327. For investment 25000 over the original half-year, the amount scales to 26041.6666667. Neither result is a current market quote or a recommendation.

January 15 to July 15, 2026 has 181 actual elapsed days:

These small differences arise from the time convention. They do not change investment cash or the stated rate. Display rounding can hide them, so retain sufficient precision while reconciling the calculation.

The official example invests 1000 on December 14, 2008, matures June 30, 2015, uses rate 6.5% and basis 0. The reconstructed 30/360 count is 2356 days:

=RECEIVED(DATE(2008,12,14),DATE(2015,6,30),1000,0.065,0)

1000/(1-0.065*2356/360) equals 1740.30745431693, matching the published value. Adding simple interest to 1000 or applying a compound-growth exponent would give a different result. The agreement is documentation-plus-math evidence, not a captured execution.

In the half-year control, the discount amount is approximately 416.6666667. Dividing by maturity cash and annualizing gives 416.6666667/10416.6666667/0.5 = 8%, consistent with the rate input.

Dividing the same gain by the original 10000 instead gives approximately 8.33333333333% simple annualized investment return. Therefore feeding an investment-return rate into RECEIVED unchanged is not a general inverse of an investment-return calculation. For comparison, adding simple interest at 8% to 10000 over half a year would give 10400, not the reconstructed RECEIVED amount.

Require 1-d*t > 0 in the positive-value model used here. As the denominator approaches zero, small changes in dates or rate can cause very large changes in the result. At zero the mathematical expression is undefined; beyond it the expression becomes negative. The checked help does not specify an exact Numbers error matrix for these boundaries, so none is invented.

Although Apple permits nonnegative investment in its parameter prose, zero-investment runtime handling was not tested. Use positive cash for the worked model. Check date order and percentage scale, and remember that region-dependent currency formatting does not perform foreign-exchange conversion. The function supplies no taxes, fees, reinvestment assumptions or independent comparison of actual securities.

The official Apple RECEIVED 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.

• RATE
• ACCRINTM
• DATE