Interest rate problem

Question

What interest rate compound monthly will yield an effective interest rate of 8%?

Answer 1

Let I = the annualized rate compounded monthly. In 1 year 1 dollar compounded monthly will be (1+i/12)^12. we want (1+i/12)^12 = (1+8%). Take the 12th root of both sides to get

1+i/12 = (1.08)^(1/12)

so i = 12*((1.08^(1/12))-1) = 7.72%.

Proof (1+(7.72%/12)) = 1.08