I N S 



168 



I N T 



the insurers commonly stipulate for a certain premium; 

 but agree, in the event of the ship sailing with convoy, 

 and arriving safe, to return so much per cent. As the 

 injured is not fully indemnified, in case of a total loss, 

 unless his property be covered, it is inferred that he 

 shoukl only be indemnified for a partial loss in the 

 same proportion ; and if his property is not fully insu- 

 red, he is considered as insurer himself for the part not 

 covered. 



Insurance transactions are commonly executed by 

 brokers, whose business it is to extend the policy, and 

 procure the subscriptions of underwriters, who seldom 

 engage for more than 200 on the same vessel. The 

 premium is paid to the broker, who accounts to each 

 underwriter for his proportion, after retaining a suit- 

 able allowance for his trouble. The various questions 

 connected with insurance are solved by the rule of pro- 

 portion, and require no elucidation. 



INTAGLIOS. See our article GEMS. 



INTEGRAL CALCULUS. See FLUXIONS. 



INTEGUMENTS. See ANATOMY, Human, vol. i. 

 p. 841; and ANATOMY, Comparative, vol. ii. p. 23. 



INTERCOLUMNIATION. See CIVIL ARCHITEO 



TURK. 



INTEREST, is a certain allowance paid by the bor- 

 rower to the lenders of money, for the use of it during 

 some specified time. The sum lent is called the Prin- 

 cipal ; the sum paid by the borrower, the Interest; and 

 both conjoined, the Amoimt. If interest, after it be- 

 comes due, be incorporated with the principal, and in- 

 terest be afterwards charged on the successive amounts, 

 it gives rise to what is called Compound Interest, to dis- 

 tinguish it from simple interest, in which the interest, 

 though foreborn, is charged only on the sum originally 

 lent. 



I. Simple Interest. 



Let p denote the principal, r the interest of 1 foi> 

 a year, ( the number of years the interest is due, and a 

 the amount for the same time ; then it is obvious that 

 a = p+prt, or a=p(l+rt), 



a a n a n 



ri . __ _ _ _ _ / _ 



' pt ~p~r~~ 



will be the 



365 



1 +>/ 



Since r is the rate of 1 for a year, 

 rate for a single day ; and therefore, if d be the num- 

 ber of days, j r will be the interest of 1 for the 

 same time. If the rate be 5 per cent, or ^, the interest 



of p pounds, for d days, will become -I51? , or 



365 ' 730O 



The interest of p for any other rate r', will evidently 

 r' pd Zr'pd TT 



X ~^, or .- . Hence we obtain the two 



be- 



7300' 



following practical rules for computing simple interest. 



1. When the rate is 5 per cent, multiply the princi- 

 pal by the number of days, arid divide the product by 

 7300. 



2. When the rate is any other than 5 per cent, mul- 

 tiply the principal by twice the rate, and then by the 

 number of days, and divide the product by 73000. 



Ex. 1. What is the interest of 456' for 85 days, at 

 5 per cent. 



Interest = 



456 X 85 



7300 



= 5:6:21. 



Ex. 2. What is the interest of 560 for 240 days, at 

 4$ per cent. 



Interest _ 



^- ?_*_ _ 16 1 1 4 3 

 73000 ^*io.U4 4 . 



When interest is calculated on a debt, discharged by Interest. 

 partial payments, it is reckoned on the several sums y< "^Y" 1 

 due, from the time of the preceding to that of the last 

 payment. This is done most convenient^ by multi. 

 plying the original sum, r 'and each successive balance, 

 in order, by the number^of days intervening between 

 the times of payment, and then dividing the amount of 

 the several products by 7300. The quotient is the 

 interest at 5 per cent. 



Ex. A bill of 6-25, due March 2, was paid up in 

 the following manner : April 10, 182 ; June 8, 25 >; 

 August 21, 96 ; and the balance, Dec. 5 ; what inte- 

 rest was due at 5 per cent. 



Days. Products. 



March 2. . . Due 625 x 39 = 24375* 



April 10. .. Paid 182 



June 8. 



D.ue 443 x 

 Paid 250 



28 = 12404 



Due 193 x 74= 14282 

 Paid (JG 



Aug. 21. . . 



Due 97 X 106=10282 

 Dec. 5. . . Paid 97 



7300)61343 



8:8:0|. 



In computing interest on accounts current, or cash- 

 accounts, the sums on the debtor and creditor side of 

 the account are added and subtracted, in the order of 

 their dates as they fall due ; the several balances are 

 then multiplied by the days as formerly, and if the ba- 

 lance be sometimes due to one party, and sometimes to 

 the other, the products are extended in separate co- 

 lumns. 



II. Compound Interest. 



Let the amount of 1 for a year, or 1 -|- r, be repre- 

 sented by E ; then, since 1 is to its amounts for a 

 year, as any other sum is to its amount for the same 

 time, 



1 : R : : R : R ? , the amount of 1 for 2 years. 



Also 1 : R'': : R : Rs, . . ' 3 years. 



Hence, it is obvious that II' is the amount of 1 for t 

 years. If the amount of P pounds, for the same time, 

 be denoted by A, we obtain 



A 



= PR', P = 



R'' 



Log. A Log. P 



~ Lo~g71l ' : 



The quantity P, or the sum which, laid out at com- 

 pound interest during t years, would amount to A, is 

 sometimes called the present value of A Thus, R' be- 

 ing the amount of I for t years, 1 is the present-va- 

 lue of R' for the same time. Since it has been already 



shewn that P = ^- f , if A be unity, or \, we obtain 



Hence the present value of l for any time /, is the 

 reciprocal of the amount of 1 for the same time. 



Calculations connected with compound interest arc 

 usually performed by help of tables, containing the 

 amount and present value of l for the requisite num- 

 ber of years. ( A ) 



INTERMITTING, or RECIPROCATING SPRINGS. 

 See HYDRODYNAMICS, vol. xi. p. 486'. 



