ANNUITIES. 209 



2. If a pension of 6ocI. per annum be forborn 5 ycr.rs, 

 what will it amount to, allowing 4 per cent, simple in- 

 terest ? Ans. 3240I. 



3. What will an.^nnuity of 250I. amount to in 7 years, 

 to be paid by half-yearly payments, at 6 per cent, per an- 

 num, simple interest ? Ans. 209 il. 5s. 



'To find the present Worth cf an Annuity at Simple Interest, 

 RULE.* 



Find the present worth of each year by itself, discount- 

 ing from the tirrie it becomes due, and the sum of all 

 these v/ill be the present worth required. 



EXAMPLES. 



* Tlie reason of this rule is manifest from the nature of discount, 

 for all the annuities may be considered separately, as so many sin- 

 gle and independent debts, due after i, 2, 3, &c. years ; so that 

 the present worth of each being found, their sum must be the 

 present worth of the whole. 



The estimation, however, of annuities at simple interest \i high- 

 ly unreasonable and absurd. One instance only will ho. sufficient 

 to shew the truth of this assertion. The price of an annuity of 

 50I. to continue 40 years, discounting at 5 per cent, will, by ei- 

 ther of the rules, amount to a sum, of which one year's interest 

 only exceeds the annuity. Would it not therefore be highly ri- ' 

 diculous to give, for an annuity to eontinue only 4O years, a suraj 

 which would yield a greater yearly interest for ever ? 



It is most equitable to allow compound interest. 



Let p = present worth, and the other letters as before. 



Then { 



nx 1 1 — ,&c. to '■ ■ z=:p. 



i-fr i-f2r i-4-3r i-{-tr 



/---^4--^+— ^.&-to ' 



14-r i4-2r 14-3^ i-{-ir 



C c 



The 



