INTEREST. 



Ex. 2 — Let n and i -(- r be the fame as above, and m = 



i 20.06, tlien will a 



120.06 X .04 



and let it be required to find m the amount of the lam p ii 

 years at the rater. Now, fiippofing the amount of i/. 



one year to be i - r, the amount of the fame fu m in t' ^_ ^^ 



years will be i + r] ; for i : i -t- r = i 4- r : I -t '1^ ^•°-+' "" ' 



In like manner i : i -j- r = l + r) : i - r] the amount Ex. l- — Putting i + r and m = 1.04 and 1 20. 06 re. 

 of 1/ in three years, and the amount of i/. by the fame r«le - -, ^ _ 



in n years will be i -(- r]". C onfcq uently the amount m of fpcftivL-ly, and a = 10, « will be — — -' ^j',, = lO. 



Viie fum />in /; years will be* . T r '!'• From this equation ' ' ^^^ 



Ex. 4 Retaining the fame values of m and a as m the 



we have^ : 



rl" 



lo g, m — \og. p - 



and 



■ — , anu r . • 120. 06I'' \ 



log. I 4- r preceding example, and putting « = 10, £ ( = ~ ' ~i ) 



be — .04146, b (= — ^ will be = 



.5454, and 



+ -04523 -•54:)4 



.,-«.) 



will 



Example. I.— Let^ = 50 . . I -t- r = 1. 04 . . n =: y- 



50, then will m (the amount of ^ol. in 30 years at J,l. per ^^= V.2cj-j^\ 



ant.) be == 50 x 1.04.]'^ = 162/. 17. be = .04. 



E.r. 2 Let m = 162/. 17. . . . n = 30 ( I -|- r = 



J53.J-, Since I + r is the amount of i/. In one year, the converfe 



1.04), the fum jl %^ ill then be =:: _1 — ^ = 50. ^ 



i-°4 r-' of this expreffion, or will be the difcountof i/. for 



Ex. 3. — Let m, p, and r be rrfpeftively equal to 162.17 ' '^ 



... JO ... and .04, Uien will n be = jj^^ j-^^g ^j^^ . f^^ if i + ;- to be received at the end of 



2.209970 5 — I.69S9700 _ ^ a year is of the fame valac with the prefent payment of i/. 



.0170333 ~ ^°' by the rule of proportion i/. to be received at the end of a 



£.?. 4.— Let m,/, and n be refpeaively equal to 162.17 ■„ , r , r 1 • t, ' A 

 year will be of the fame value with • now received, 



. . . CO . . . and 30, and r will be equal to ' -*-•' ' j r5 



50 i 

 — I = ■04- 



As the amount of i/. in n years is i n- rj", the amount 

 of the fame fum in n — i years will be i J- r]''"',in h — 2 in 



years i + 'r\"~-, &c. ; therefore, if i/. be the amount at ^ i ■ - 1 ■ i 

 the end of t he firfl: year, the feries i -j- i + r + i + r\' -f received at the end of two years, and hence = 

 I + rj"^' will exprefs the amount of i/. per ' + ''I 



+ ,.)■■ _ , the prefent value of i/. to be received at the end of n years, 

 the value of the fum a, therefore, to be received at the end 



that is, I + »■ : 

 + '■ : I = 



By the fame reafon- 

 the value of i/. to be 

 will be 



annum in n years, which may eafily be found — ^ "^ '" 



and m (the amount of the annual fum a) will be = 



^' ^ "*" ' , hence a will be :=- . -^ » and n = 



1 + rC 



of n years will be ^ w = tt ; from this equation the 



value of a will be found = rr . i -f- r]", the value 



log.) 



I02. I 



of 



„ = '^g^-JfSlII.andtl 



In order to find the value of r, let the binomial i 4- 

 be expanded, &c., and — will be = j + — — r 



le value of r = "[» 



4- &c. and J!L I. .-I _ 



log. 



1 r 4- Exdwpk I.— Let n be = 20 . . « = 40 . . T~+~r =z 

 20 

 1.06, andT= 7;^*'= '•944- 



Ex. 2. — If ff = 1-944, I 4- r = 1.06, andn = 40, g 



' "^ *■ + ('= ITSf^^ X 1.944") will be = 20. 



'^- — • .r* nearly. Put 1 = <-, and =i,thi 



■will rbe= \ ib + 26 c 

 Example I. — If a — ic 



J.04, m will be = — 



.04 



Vol. XIX. 



Ex. 3. — Retaining the values of t and i + r, and put- 



.„ , 1. 3010? — .28878C6 

 ;inff a — 20, « will he—^ "^ ^-i- = 40. 



fa .0253059 



Ex. 4. — If T = 1.944 . . a = 20, and n = 40, i» 



(= -^° h' - i ") will be = .06. 



