We will show that continuously compounded interest is a limiting case, as n , of periodically
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We will show that continuously compounded interest is a limiting case, as n → ∞, of periodically compounded interest. We first establish an important limit.
(a) Show that ln(1 + r) is the area under the graph of y = 1/x from 1 to 1 + r.
(b) Using rectangles with base length r, prove that
(c) Prove that
(f) Prove that for an interest rate r, continuous compounding of interest is the limit as n → ∞of n-times annual periodic compounding of interest.
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