INTEREST. 



tliey are a, I, e, J, Sec refpecttvely, and the whole amount 

 of them be p, the time / will be = 



log. p - log. ( -—-^ + -p^, + ==,, + &c.) 



log. I + r 



Ihcorsm 7. — Suppofing the fum b to be now borrowed 

 on condition that the annuity c (houlj be paid in difcharge 

 of it, after the expiration of n years ; for liow many 

 years / Ihould fuch afinuity be continued from that time 

 fo as to be an equivalent to the lum fo advanced ? 



Sohit'wn. — The amount of ^ in « years being b . l+r\' 

 and the value of the annuity c for / years being 



Z__L ~ — , thcfc two expreffions, by the condi- 



3650o)96774( 3/. 13/. c\d. Brought 

 7^000 



20 Shillings 



tion of the problem, will be equal to each other. Let 

 - be denoted by d, then may / be eafily 



1 J-. d 



log. 



400 



Thus, if* = 1032 c ^ i, 



and r = .0^, d will be 

 46.4, and t 



400 — ..05 X 1032 X 6.0S 



-^ — ^!_ll = q 1.4, that is, if 1052/. be now borrowed 

 log, of 1,05 o t' > i 



on condition that the debt (hould be difcharged at the 

 end of 37 years by an annual payment of 400/. fuch pay- 

 ment, computing at 5/. per cent, fhould be continued for 

 31I years. . . 



Corollary. — If c be = I + r]" X i r, the annual pay- 

 ment mull be continued for ever ; if » be lefs than b r x 

 1 -f ;-| ", the debt can never be repaid. 



From any four of the above quantities being given the 

 fifth may be obtained without much diiSculty. But it 

 cannot be neceflary to purfne this fubjedl further, as the 

 folution of thefe or any other cafes in compound intereil 

 may be eafily derived from the principles already explained 

 in this article. 



See on this fubjeft, Jones's Synopfis Palmariorum Mathe- 

 feos, part. i. feft. 3. chap. 10. Gardiner's Tables of Lo- 

 garithms, p. 13. 3d edition. Philof. Tranfaftions, vol. Ix. 

 p. joS. and vol. Ixvi. p. 109. Taylor's Tables of Loga- 

 rithms, p. 30; and Mazere's Scriptores Logarithmici, vol. v. 

 p. 220. See alfo Annuities Certain, and Discount. 



A mercantile friend has favoured the editor with the fol- 

 lowing univerfal rule for finding tlie intereft upon any fura at 

 any rate, for any number of days. 



Multiply the fum by the rate of intereft, and multiply that 

 product by the number of days ; then divide that produA by 

 36500. The quotient will be the anfwer. 



Now fuppofe the queftion to be, What is the intereft upoa 

 127/. at 3,1. per cent, per annum for 254 days I 

 ■ £. £. 



127 at 3 for 254 days. 

 3 Rate of intereft, 



381 Firft produdl. 

 254 Days. 



H0480 



109500 



980 

 12 Pence. 



11760(0 



4 Farthings. 



47040(1 

 365CO 



10540 Remainder. 



It is evident, that in multiplying 127 by 5, according to 

 the Jirjl operation of the rule, the amount is increafed one 

 liundred times too much, for the produdl 3S1 is only three, 

 and eighty-one hundredths, or 381/. which is equal to 

 7,1. \6s. 2ld. or the intereft of 127/. at 3 percent, for one year. 

 Therefore, to correft this_yCr^ error, the produdl 381 muft 

 be divided by 100, and it will be right. 



But in following the rule, the _^r/} error is continued, and. 

 we go on to multiply that product by the number of days, 

 by which it is alfo evident that the produft 96774 includes 

 a Jccond error of 365 times (too much, being for days inttead 

 of for years, and the amount of the two errors taken togetlier 

 is 100 times 365 times too much, or 36,500 times too much, 

 therefore, to bring it right, it muft be divided by that 

 number. 



This explains the principle of the firft nnivcrfal rule, 

 which requires three operations, becaufe it is adapted to any 

 rate of intereft whatever. 



To find the intereft upon any fum at 5 per cent, for any 

 number of days : 



Rub. — Multiply the fum by the number of d.-ivs, ani 

 divide the produft by 7300. 



Example. 

 What is the intereft upon 2745/. for 365 days? 

 365 



1372J 

 16470 

 8^3) 



^300)1001925(13; 



7300 



27192 

 21900 



1524 



J905 

 762 



£. s. d. 



365oo)96774( 2 13 o^ Anfwcj". 



365oo(^ 

 36500 



latereit 



