In 1978, a New York State Assembly-woman wrote a letter to her constituents about electric rates. She wrote: "If the commission grants this increase, it will mean that between 1970 and 1987, the electric rates will have increased by more than 478 percent. That's an average rise of over 27 percent a year!" Is this correct? If not, what annual percent increase over 17 years leads to a total increase of 478 percent?

Question

In 1978, a New York State Assembly-woman wrote a letter to her constituents about electric rates.  She wrote: "If the commission grants this increase, it will mean that between 1970 and 1987, the electric rates will have increased by more than 478 percent.  That's an average rise of over 27 percent a year!"  Is this correct?  If not, what annual percent increase over 17 years leads to a total increase of 478 percent?

anonymous · Answer

$$(1+r)^{27}=4.78$$ solve for r