solve for x: 100(1+.04)^5 = 118.5(1+x)^5

Question

where x is the interest rate

Answer 1

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%