IXTF.KEST. 



INTEREST. 



HI 



Catholic writer*. In ooune of time the measure was found no longer 

 to answer iU object, and it became of rare occurrence. Paul V., in 

 April, 1606, laid the republic of Venice under an interdict, because the 

 noate had decreed that no more convent* should be founded, and 

 no more property should be bequeathed to monastic orders without 

 perraismion from the government. The senate forbade the bull of 

 interdict to be published in the territories of the republic, ami ordered 

 the parochial clergy to continue the exercise of their sacred ministry as 

 usual. The Jesuits, Franciscans, and other monks pleaded their duty 

 of obedience to the see of Rome, and the senate told them that they 

 might depart, which they did. At last, in 1607, through the media- 

 tion of Henry IV. of France, the pope removed the interdict, which 

 had produced little or no effect on the minds of the Venetian people. 



INTEREST, money which is paid for the use of other money, the 

 lender stipulating for a fixed sum to be paid yearly, half-yearly, or 

 quarterly, for each 1001. lent, until the money is returned. When this 

 U not the case, and when the money paid for the loan depends upon 

 the success of an undertaking, or any casualty not connected with the 

 duration of life, it is called a dividend ; when the money and its 

 interest are to be returned by yearly instalments, and paid off in a 

 certain fixed number of years, it is called an annuity cert 'in; but when 

 the payment is to depend upon the life of any person or persons, it is 

 called a life annuity. [ANNUITY.] But by whatever name the pro- 

 ceeds of money may be called, the rules of calculation are the same in 

 every case but that of a life contingency. 



A simple rule for converting shillings, pence, and farthings into the 

 decimal of a pound, alluded to in the article ANNUITIES, might be 

 made of such frequent use in calculations connected with interest, that 

 we begin with it. The rule is founded upon the circumstance of one 

 farthing being very little more than the thousandth part of a pound. 



To convert any number of shillings, pence, and farthings to the 

 H<iiil of I/., as far as three places. 



UULE. Allow 100 for every two shillings, and 50 for the odd 

 shilling, if there be one, and a unit for every farthing in the pence and 

 farthings, adding 1 if the pence and farthings be sixpence or upwards. 

 Then make three decimal places of the result. Thus, It. 7 jrf. give 50 

 and 31 and 1, or 82, which, converted into a decimal of three places, is 

 082, or It. 7 jd. is -0821. : the truth lies between -0822 and -0823. 

 Again, 17. 44''. give 800 and 50 and 18, or -868, so that 17s. 44d. is 

 868t very nearly. 



To convert any decimal of a pound of three places into shillings, 

 pence, and farthings. 



RULE. Take away the decimal point, and make a whole number of 

 the three places : for every 100 of this whole number allow two 

 shillings, and another shilling to the remaining 50, if so much remain 

 Let every unit of the remainder be one farthing, but strike off one il 

 the remaining number exceed 24. Thus, '973/. gives 18*. and Is. and 

 23 farthings, or 19*. 5jd. ; but -147t gives 2. and 46 farthings, or 

 2*. 114d. The following are examples of both rules : 



6}d. is -028/. 

 3*. Id. is -1581. 

 4*. 9|d. is -23S/. 



16. 04d. is -802/. 

 17.. lid. is -895t 

 19. H>4d. is -993t 



This rule may be completed, HO as to give any number of places, as 

 follows : For the fourth and fifth places of decimals, allow 4 for every 

 farthing above the last sixpence, with a unit additional for every six 

 farthings. Thus, for 2*. SJrf., the first three places being '122, the 

 fourth and fifth places are found by 22 x 4 + 3, or 91. For the sixth am 

 all following places, take the number of farthings above the last three 

 halfpence for a numerator, 6 for a denominator, and form the figures 

 of the corresponding decimal fraction. In the above instance we have 

 |, or -0666 whence 2t 5Jd. is -1229166661 



Interest is usually reckoned by the sum paid yearly for each lOOt , 

 thus, 4 per centum, abbreviated into 4 per cenl., means that 41 is pau 

 yearly for 10W., or that ,',th of the whole sum is paid yearly fur its 

 use. In some cases, as in the dividend of a bankrupt's estate, a part is 

 compared with the whole by stating how much of each pound is paid 

 The preceding rule gives the means of reducing one to the other install 

 toneously : thus,since 4. 9Jd. is -238/., a bankrupt who pays the former 

 urn per pound, or -23bV. for II., pays 23'8/. for each 100/., or 23( per 

 cent Similarly, 87& per cent, or S7'2t for 1001., is -372t for It, or 

 7> 64d. in the pound. 



Interest U called timpU when it is paid as soon as due, or when 

 if deferred, interest is not charged upon interest But when the lattc 

 charge U made, the interest is called cum.mund. In simple interest i 

 makes no diderence whether it be payable yearly or at shorter terms 

 but thu is not the cae in compound interest. The sum lent is callet 

 the pri ,ri/,al ; and the princiful. together with the interest, the 

 am iunt ; also, the principal ia called the preterit value of the amount 



A common question of simple interest requires merely the process 

 of taking a given fractional part of a sum of money, ancf need not be 

 explained at length in a work of reference. One example, however 

 will serve to show the facilities which the preceding rule a..ords. 



What U the interest upon 697*. 18*. 44*., at 44 per cent, for 7} 



'.'''' ' 



To find this, we must take the hundredth part of the sum 44 times 

 for one year's interest, which we must then repeat 7| times. 



697 13*. 44d. 



i 697-668 

 4* 



2790672 

 848-884 



100)8189-606 



31-39506 or 31-89506 



219 76542 



15-69753 



7-84877 



24381172 

 Answer 243-812 or 243 6s. 3d. 



251-16048 

 7-84877 



243-31171 



When interest is to be taken for a number of days, a person who is 

 often required to perform the operation will provide himself with a 

 set of tables, several of which are published. Those who do not often 

 meet with the operation must take such a fraction of a year's interest 

 as the number of days in the question U of a year. The following 

 rule will facilitate the introduction of the arithmetical rule of 

 practice : 



RULE. Whenever the portion of an amount per annum is to be 

 taken corresponding to a number of days, calculate as if the year had 

 only 860 days, and from the result subtract its 72nd part, or one 

 farthing in 1>. 6rf., or 34d. on each guinea. This falls short of the 

 truth by about Id. in 20k Thus, suppose the yearly interest is 

 283t 17. id., and that for 254 days is required 



283-866 



180 ..}... 141938 

 60 . . I . . . 47-311 ' 

 12 . . I . . . 9-462 

 2 . . . . . 1-577 



8)200-283 

 9) 25-035 



2-782 

 200-283 



197-501 



Answer, 197*. 10*.;- or, adding Id. for each 20t, about 197t 10.10d., 

 which is within one halfpenny of the truth. 



It is sometimes necessary to express the interest by the day, in which 

 the following rules will be convenient : 



To turn a given amount per day into the corresponding amount per 

 year, to the number of pence per day add its half, and take as many 

 pounds aa there are now pence. This is the amount in 360 days, and 

 five days' allowance added gives the result. 



To find out how much a sum per annum yields per day, subtract 

 one-third from the pounds, and take as many pence as there are in the 

 result. The answer is the preceding result diminished by one farthing 

 in 1. 6d., or its 72nd part. 



Thus, 3|rf. per day, or 375 pence, gives 875 + 1-875, or 5-625 per 

 360 days, which is 51. 12. 6d. To this add five times 3}<<., or Is. 6 jrf., 

 which gives 51. 1 4s. 0|d. per annum. 



Again, 261. 14. 7d. per annum, or (nearly enough) '2671., gives 

 26'7 8'9 pence per day nearly; that is, In. 5|d. Diminish this by 

 one farthing, and Is. 5^d. is the answer within a farthing. 



All persons who attempt for the first time to use decimal fractions 

 in money computations imagine that they gain nothing ; but a little 

 practice soon convinces them of the contrary. 



We now proceed to the subject of compound interest, which cannot 

 be satisfactorily treated without algebra. Let r be the interest of U. 

 for one year, or 100 r the rate per cent. As follows : 



At 2| per cent. r = '0225 

 At 34 per cent. r= -035 



At 4 percent. r=-04 

 At 6J per cent. r= -U5125. 



It is not usual in treating of compound interest to separate that part 

 of the amount which is interest from the whole. We shall, therefore, 

 speak only of principal and amount, or, when the latter is the given 

 sum, of present value and deferred principal. Hence, 1 + r is the 

 amount of I/, in one year, 2 -f 2r that of 21. in one year, and, generally, 

 a sum which is a pounds at the beginning of any one year becomes 

 o(l + r) pounds at the end. 



Consequently, the amounts of It at the end of one, two, three, ic., 

 years, are 1 + r, (1 * r)*, (1 + r), &c., pounds ; and II. at the end of n 

 yean becomes (1 + r)" pounds. If, then, a becomes i A in n years, at 

 r per pound, we have 



A = o (1 r) a 



