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Calculus/Continously compound interest

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Expert: - 9/15/2008


Question
Suppose that you discover in the attic an overdue library book on which you grandfather owed a fine of 30 cents 100 years ago. If an overdue fine grows exponentially at a 5% annual rate compounded continously, how much would you have to pay if you returned the book today?

I know that the rate is 1.05 and that a point is x(100)=.30 but am not really sure how to go from there. Any hints?

Answer
If the interest rate is 0.05 and is compounded anually, take 1.05 to the number of years and multiply by the base amount.

This means you take (30 cents)1.05^100.

If you just looked at this and wanted to approximate it, it would double about every 14 years.  This means it has doubled over 7 times.
The number 2 to the 7th is 128, so a rough guess on the amount owed would be $39.

If that were me, I would go check the library.  They probably don't care about the book any more.  If they do, it might be cheaper to look on e-bay and find one for sale...

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