To accumulate $8000 at the end of 3n years, deposits of $98 are made at the end of each of the first n years and $196 at the end of each of the next 2n years. The annual effective rate of interest is i . You are given (l + i)n = 2.0 . Determine i . Thanks in advance!
Accumulated value of the annuity after n years: = 98* ((1+i)^n - 1)/i = 98* (2-1)/i = 98/i {Since (1+i)^n = 2} => Accumuated value of this annuity after 3n years = (1+i)^2n * 98/i = 4*98/i = 392/i ----> eq1 Accumulated value for 2nd annuity of 196 for 2n years = 196*( (1+i)^2n - 1)/i = 196*(4-1)/i = 588/i ----> eq2 Summing eq1 and eq2 and equating it to 8000, 8000 = 392/i + 588/i => 8000 = 980/i or i = 12.25%
