solve for x: 100(1+.04)^5 = 118.5(1+x)^5, where x is the interest rate.
100(1+.04)^5 = 118.5(1+x)^5
((1+x)/(1.04))^5 = 100/118.5
Taking logs of both sides,
5.ln((1+x)/1.04) = ln(100/118.5) = -0.169742
ln((1+x)/1.04) = -0.169742/5 = -0.033948
Taking exponents of both sides,
(1+x)/1.04 = e^(-0.033948) = 0.96662
1 + x = 1.005286
x = 0.005286
Answer: x = 0.53%