Kristen can invest $30,000 in two options:

(i) deposit 30,000 into a fund earning an nominal interest rate k compounded quarterly or

(ii) purchase an annuity-immediate with 20 annual payments of X at an annual effective rate of 10%, immediately after receiving each payment X from the annuity-immediate, Kristen deposits it into a fund earning an annual effective interest rate 8%. Find k if both options produce the same accumulated value at the end of 20 years