A boy invests a sum of $4000 on his 10th birthday in the year 1996, with an annual interest rate of 7%, compounded every six months. During some stage of the investment, the interest rate changes to an annual rate of 6%, still compounded every six months. On the boy's 18th birthday, the boy checks his account to see a sum of $6770. At what point in time did the interest rate change from 7% to 6%?

(In reply to

analytic solution by Charlie)

I agree with your result. When the calculations are rounded, the answer is that the interest declined to 6% 5.5 years after the boy's 10th birthday.