202 ARITHMETIC. 



2. Suppose 400I. are to be paid at the end of 2 years, 

 and 2 1 col. at the end of 8 years ; what is the. equated 

 time for one payment, reckoning 5 per cent, simple inter- 

 est ? Ans. 7 years. 



3. Suppose 300I, are to be paid at one year's end, and 

 300I. nfore at the end of i^ year ; it is^ required to find 

 the time to pay it at one payment, 5 per cent, simple 

 interest being allowed. Ans. 1*248637 year. 



COMPOUND INTEREST. 



Compound Interest is that, which arises from the 

 principal and interest taken together, as it becomes due, at 

 th- end of each stated time of payment. 



I RULE.'^' 



I. Find the amount of the given principal, for the time 

 of the first payment by simple interest. 



2. Consider 



The equated time for any number of payments may be readily 

 found when the question is proposed in numbers, but it would not 

 be easy to give algebraic theorems for those cases, on account of 

 the variation of the debts and times, and the difficulty of finding 

 between which of the payments the equated time would happen. 



Supposing r to be the amount of il. for one year, and the othw 



/oo-.^r^-f"^ 

 er letters as before, then / — s will be a general theorem 



log. r 

 for the equated time of any two payments, reckoning compound 

 interest, and is found in the same manner as the fQ|mer. 



* The reason of this rule is evident from the definition, and 

 the principles of simple interest. 



