ACTSC231 Lecture Notes - Interest, Compound Interest, Discounting
11 May 2014
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Document Summary
To accumulate the money over the nth year we multiply by 1+in! For simple interest a(t) = 1+rt! i1 = [a(1)-a(0)]/a(0) = (1+r-1)/1 = r! So r is the effective rate of interest in the 1st year. i2 = r/(1+r)! i3 = r/(1+2r)! in = r/(1+r(n-1))! Example: find the yearly simple interest rate so that investment at time 0 will grow to. in 8 years! slon: 1000(1+8r) = 1700 => r = 0. 875! This is the amount of interest earned in any year. If the annual effective rates on interest are all consistent, i. e. i1=i2=i3= ,! then we could drop the subscript! a(n) = (1+i)^n, for n = 0,1,2 ! usually we assume a(t) = (1+i)^t for t >= 0! We call this compound interest. in = [a(n)-a(n-1)]/a(n-1) = [(1+i)^n - (1+i)^(n-1)] / (1+i)^(n-1) = i for n=1,2,3 ! This annual effective rate of interest over (t,t+1)! i[t,t+1] = [a(t+1)-a(t)]/a(t) = i! (1+i)^t a(t)
