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Continuously Compounded Interest. A Limit Involving e Numerically evaluate the following limit: x 101001000 10000 100000 1000000 10000000 f(x)f(x) 2.5942.7052.7172.718.

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Presentation on theme: "Continuously Compounded Interest. A Limit Involving e Numerically evaluate the following limit: x 101001000 10000 100000 1000000 10000000 f(x)f(x) 2.5942.7052.7172.718."— Presentation transcript:

1 Continuously Compounded Interest

2 A Limit Involving e Numerically evaluate the following limit: x f(x)f(x)

3 Compound Interest P = Principal Amount (original) r = decimal rate ( % ÷ 100 ) t = time in years n = number of intervals

4 A Limit Involving Compound Interest Analytically evaluate the following limit: Rewrite the limit so it resembles the limit involving e. Let x = n/r. This limit represents interest that is compounded infinitely many times a year (continuous).

5 Continuously Compounded Interest P = Principal Amount (original) r = decimal rate ( % ÷ 100 ) t = time in years


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