In 1958, a first-class postage stamp for a 1-ounce envelope was $0.04. In 2012, a first-class postage stamp for the same envelope is $0.45. What was the annual compound increase in the cost of the first-class postage during the 54 year period

The annual increase was approximately $0.002

Explanation:

In order to know the annual compound increase in the cost of the first-class postage during the 54 year period, we need to know the rate at which the compound interest was calculated. We can know that using the following compound interest formula:

P = principal amount (the initial amount for the envelope)

r = annual rate of increase

t = number of years the amount is increased.

A = amount of money accumulated after n years, including the increase.

Now, we have our Amount at the 54th year to be 0.45dollars, when the principal is 0.04dollars.

Therefore, we have

A = $0.45

P = $0.04

r = unknown (that's what we are looking for)

t = 54

Substituting these into the formula, we have:

Dividing both sides by 0.04 we have:

Taking the 54th root of both sides we have(approximately):

The above gives:

This gives:

Therefore, the money increased annually at the rate of 5% approximately, and that would be

Which is $0.002 approximately.

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