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Mathematics - Calculus

Suppose that interest on money in the bank accumulates at an annual rate of 5% per year compounded continuously. How much money should be invested today, so that 20 years from now it will be worth $20,000?
(Hint: If you're stuck, then model the account balance B= B(t) with a differential equation and an initial condition, keeping in mind that the initial condition here is not at t=0)
A. $5498.23
B. $6766.49
C. $7982.22
D. $7357.59
E. $5909.04

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  1. I think its answer D but I am not sure.

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  2. yea it was that

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  3. A e^rt = 20,000
    A e^.05*20 = 20,000
    ln A + 1 = 9.903
    ln A = 8.903
    A = 7357.59

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  4. p * e^(rt) = 20000

    p = 20000 / [e^(.05 * 20)] = 20000 / e

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