825 



INTEREST. 



INTEREST. 



TABLE V. 

 THE AMODXT OF 1 PER AXNU* ix ANY NTTMBER OP YEARS. 



at the second payment, &c., and II. at the nth and last payment is 

 worth 



(1-rf 



and, reversing numerator and denominator, we have the fraction of II., 

 which must be paid at the end of the first year, in order to repay 11. 

 now lent, by uniformly decreasing instalments in n years. 



All the preceding formulae are easy to compute by aid of logarithms, 

 and the result of any one being given, and the rate of interest, it is 

 easy to determine (except in the two last formulae) the number of 

 years necessary. But if the number of years be given, and the result, 

 and it ia the rate of interest which is unknown, an equation must be 

 olved, the degree of which is at least as high as the number of years. 



When the interest is to be paid at the expiration of a fraction of a 

 year, it is the same thing as if a less rate of interest were paid for a 

 greater number of years. In the preceding investigations 1 + r may 

 be considered as the amount of II. at the end of a term, and n as the 

 number of terms. If then quarterly interest be paid during n years, 

 r per pound per annum gives Jr per pound per quarter, which con- 

 tinued for 4ra quarters gives (1 + Jr) 4 for the amount. 



The tables appended to this article are intended to save the trouble 

 of calculation in ordinary cases. They extend from 2 4 to 6 per cent. 

 Higher rates are occasionally useful, but it is to be remembered that 

 when the rate of interest is high, and the number of years not small, 

 tablet of yearly interest become sensibly incorrect when the money is 



really improved half-yearly or quarterly. Thua the tables at 6 per 

 cent., with double the number of terms, will better represent the 

 actual progress of money at 10 per cent, than the common yearly 

 tables. The calculator who wishes to meet every case with readiness, 

 must make himself independent of particular tables. This can be 

 done with the common seven-decimal tables of logarithms, up to five 

 places of decimals and 100 years : and if the logarithm of 1 + r be 

 given to ten places of decimals, up to seven places and 1000 years. 

 The following subsidiary table is therefore given, which contains the 

 logarithms of 1 + r, for every quarter per cent, up to 6 per cent., and 

 to ten places of decimals. (See INTERPOLATION for a simple method of 

 finding intermediate logarithms.) 



