find the interest rate

Question

chirs plans to invest 500$ in his account. find the interest rate needed for the money to grow to 1300 in 16 years if it is compounded quarterly

Answer 1

500$ at x%, 16 yeers, kompound bi quarters...want 1300$ . . . 1300/500=2.6=(1+x/4)^4*16 . . . 2.6= (1+0.25x)^64 . . . log(2.6)=64*log(1+0.25x) . . . log(1+0.25x)=log(2.6)/64=0.414973348/64=0.006483958562 . . . 1+0.25x=10^0.006483958562 =1.015041872 . . . 0.25x=0.015041872 . . . x=4*0.015041872 . . . x=0.060167488.... 6%