AXNUIT 



213 



2. Div'iuc the annuity by the square of the r:ulo, and 

 ^he quotient will be the present worth cf the annuity for 

 two years. 



3. Find, in like manner, the present worth of each year 

 by itself, and the sum of all these will be the value of the 

 annuity sought. 



EXAMPLES. 



or principal of this, according to the principles of compound In- 

 terest, Is the amount divided by r, therefore 



r" — I , r'-l-T — / 



«X -7- r -py and/ X -r^ =«. 



r'-j-l — r^ r — I 



And from these theorems all the cases, where the purchase of 

 annuities is concerned, may be exhibited in logarithmic terms, as 

 follows : 



I, Z^^. n-^Lcg. I — — Log, r — i~Lcg.p, 



II. Log. p-^- Log. r — I — Log. I — — "TzI^ng. n. 



III. — £ 1 — JX.^.JL^zz.t. IV. r-'^ — ---fi X/-/ + — =ro. 



Log.r P p 



Let t express the number of half years or quarters, n the half 

 year's or quarter's payment, and r the sum of one pound and \ or 

 i" year's interest, then all the preceding rules are applicable to 

 half-yearly and quarterly payments, the same as to whole years. 



The amount of an annully mciy also le found for years and parts of 

 a year, thus : 



1. Find the amount for the whole years as before. 



2. Find the Interest of that amount for the given parts of a 

 year. 



3. Add this interest to the former account, and it will give the 

 whole amount required. 



ne 



