Use both interest conversion approach and algebraic approach to nd the accumulated value 18 years after the rst payment is made of an annuity on which there are 8 payments of $2000 each made at two-year intervals. The nominal rate of interest convertible semiannually is 7%. Answer to the nearest dollar.

The answer:

The nominal rate of interest convertible once every two years is j, so that 1+j = (1+.07/2)^4 and j=(1.035)^4 -1= .14752

The accumulated value is taken 4 years after the last payment is made, so that

2000s_8Ij (1+j)^2= 2000(13.60268)(1.31680)= 35824

I do not understand the part why it has to time (1+j)^2 in 2000s_8Ij (1+j)^2 parts. Instead of just 2000s_{8Ij .} Can I have a detail explain to this. Thank you