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F ederal R eserve Bank of New York rC irc u la rN o . 6 6 6 4 ~ 1 u D ecem ber 28, 1970 J REGULATION Q Amendments and Interpretation on Payment and Computation of Interest To A ll Member BanTcs, and Others Concerned, in the Second Federal Reserve District; Enclosed is a copy of amendments, effective January 1, 1971, to Regulation Q, “ Interest on Deposits,” of the Board of Governors of the Federal Reserve System. The amendments authorize the use of a 360-day basis in computing simple daily interest for a deposit with any m aturity and permit the advertisement of the percentage yield resulting from the use of that basis. In addition, printed below is the text of a related interpretation of Regulation Q by the Board of Governors, indicating that a member bank may use the 360-day basis in compounding interest daily or continuously on time and savings deposits. An earlier version of the amendments was submitted by the Board of Governors for public comment in October; the text of that version was sent to you in our Circular No. 6620, dated Oc tober 19, 1970. Additional copies of this circular and its enclosure will be furnished upon request. A lfred H ayes, President. [Reg. Q] P a rt 217 — INTEREST ON DEPOSITS Payment and Computation of Interest § 217.151 Payment and computation of interest on time and savings deposits. T he B o a rd has expressed th e follow ing views re la t in g to th e p ay m e n t an d co m p u tatio n of in te re st on deposits. (a ) T he m axim um ra te of sim ple in te re st th a t a m em ber b an k m ay p ay on a deposit is established by § 217.7 of R eg u latio n Q. I n J a n u a r y 1970, th e B o ard p u ted , R is th e a n n u a l ra te of sim ple in tere st and T is th e tim e period. E ffective J a n u a r y 1, 1971, § 217.3(e) of R egulation Q w as am ended to authorize th e use of 360 o r 365 (or 366 in a leap y e a r) as the d enom inator of a fra c tio n in w hich th e n u m e ra to r is th e a ctu a l n u m b er of days th e deposit earn s in terest. F o r exam ple, a b ank w ould be p e rm itte d to consider th e tim e fa c to r on a 295-day deposit a s-^ -o r On a 360-day deposit, the fra c tio n could be established c e rta in ra te s on deposits w ith a m a tu rity of “ one y e a r or m o re .” To q u a lify fo r a ra te th a t m ay be p a id on such a deposit, th e deposit m ust not - S ~ o rl S r J [t could n o t b e ^ S " • A d d itio n ally , § 217.3(e) authorizes in th e n u m e ra to r of th e tim e m a tu re b efore one fu ll y e a r — 365 o r 366 d ays as the fra c tio n th e use of 30 days (o r m u ltip les th e re o f) for case m ay be — fro m th e d a te of d ep o sit.1 deposits of one m onth (o r corresponding m ultiples (b ) T he fo rm u la fo r th e co m p u tatio n of sim ple in te re st is A = P (1 -f- R T ) w here A is th e final th e re o f). F o r exam ple, on a deposit m ade F e b ru a ry 1 fo r one m onth, th e tim e fra c tio n could be sta ted as am ount, P is th e am o u n t on w hich in te re st is com 1 In the area of consumer time deposits (deposits in denominations of less than $100,000), under $217.7 in effect in December 1970, a member bank may pay 5 per cent interest on a deposit that matures 3 months from the date of deposit. If the date of deposit is in February, such deposit will mature in 89 days. The Board regards this de minimis departure fom the 90-day interval required for payment of interest at 5 per cent (12 CFE 217.144) as justified on the grounds of mathematical simplicity. (oveb) (c) S ection 2 1 7 .3 (a) p ro v id es th a t th e effects of com pounding m ay be d isre g a rd e d in d eterm in in g (d ) The fo rm u la fo r o th er th a n continuous com p o u n d in g is A = P (1 + R /M ) N w here A is the final w hether a m em ber bank is p a y in g in te re st in excess am ount, P is th e am ount on w hich in te re st is com of the ra te s established in § 217.7. T he fo rm u la fo r pounded, R is th e a n n u a l ra te of sim ple in terest, M continuo u s com pounding is A = P e RT w here A is th e is th e n u m b er of com pounding periods in a year, an d final am o u n t, P is th e am o u n t on w hich in te re st is N is th e a c tu a l nu m b er of periods fo r w hich in te re st com pounded, e is th e base fo r N a p ie ria n o r n a tu ra l is com pounded. W h en com pounding in tere st q u a r logarithm s, R is th e a n n u a l ra te of sim ple in terest, te rly , M = 4 ; com pounding m onthly, M = 12; and a n d T is th e tim e period. T m ay be expressed as a com pounding daily, M = 360, 365, or 366. F o r ex fraction in w hich the n u m e ra to r is th e a c tu a l nu m ber am ple, a b ank m ay com pound 5 p e r cent in terest daily of d ay s th e fu n d s e a rn in te re st a n d the den o m in ator on a $10,000 deposit fo r 91 days in accordance w ith m ay be e ith e r 360, 365, or, in th e case of a leap year, eith e r of the fo llo w in g : 366. A s is p e rm itte d in sim ple in te re s t calculations, a A = $10,000 (1 + .0 5 /3 6 0 )91 or $10,127.18; or bank m ay consider each m onth as h av in g 30 days. A = $10,000 (1 + .0 5 /3 6 5 )91 or $10,125.43. (Interprets and applies 12 U.S.C. 371b and 461.) B oard of G o vernors of t h e F ed er a l R e serv e S y s t e m IN T E R E S T O N D E P O S IT S A M E N D M E N T S TO R E G U L A T IO N 0 1. E ffective J a n u a r y 1, 1971, § 217.3(e) is 2. E ffective J a n u a r y 1, 1971, § 217.6(b) is am ended to rea d as fo llo w s: am ended to re a d as fo llo w s: S E C T IO N 217.3— IN T E R E S T ON T IM E S E C T IO N 217.6— A D V E R T IS IN G O F A N D S A V IN G S D E P O S IT S IN T E R E S T ON D E P O S IT S * * * * (e) C o m p u ta tio n of in te re st. I n th e com p u ta tio n of sim ple d a ily in te re st, th e tim e fa c to r should be expressed as a fra c tio n in w hich th e a c tu a l n u m b er of days th e fu n d s e a rn in te re st is th e n u m e ra to r, a n d th e de n o m in ato r is e ith e r 360, 365, or, in a leap year, 366. H ow ever, w hen a deposit m a tu re s in one m o n th (or m u ltip les th e re o f), th e b an k m ay use 30 days in th e n u m e ra to r (o r co rrespond in g m u ltip les th e re o f). # * * # (b) P e rc e n ta g e yields based on one y ear. W here a p ercentage yield achieved by com p o u n d in g in te re st d u rin g one y e a r is a d v e r tised, th e a n n u a l ra te of sim ple in te re st shall be sta te d w ith equal prom inence, to g e th e r w ith a reference to th e basis of com pounding. No m em ber b an k shall advertise a percen tag e yield based on the effect of grace periods p erm itte d in § 2 1 7 .3 (d ). * ^ P R IN T E D IN N E W YORK