Question

Deposits of $79 are made at the end of each year for n years and $158 at the end of each year of the next 2n2n years.
The AV of this annuity at the time of the last payment (i.e. at the end of 3n years) is $7000. The annual effective rate of interest is such that (1+i)^n=1.3, Determine i.

Answer 1

7000=(79/i*(1-1/(1+i)^n)+158/((1+i)^n)*(1-1/((1+i)^(2n))))*((1+i)^(3n))

=>7000=(79/i*(1-1/1.3)+158/1.3*(1-1/(1.3^2)))*(1.3^3)

=>i=0.5812%

=>n=log(1.3)/log(1+0.5812%)=45.27288