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  1. #1
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    differential word problem

    Suppose that we want a certain endowment to pay 50,000 dollars in cash ten years from now. The endowment will be set up today with 5,000 dollars principal and locked in at a fixed interest rate. What interest rate (compounded continuously) is needed to guarantee the desired payoff?

    I know that Amount = P(1+(r/100n)^(10n) but I can't figure out the rate.
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  2. #2
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    Quote Originally Posted by keemariee View Post
    Suppose that we want a certain endowment to pay 50,000 dollars in cash ten years from now. The endowment will be set up today with 5,000 dollars principal and locked in at a fixed interest rate. What interest rate (compounded continuously) is needed to guarantee the desired payoff?

    I know that Amount = P(1+(r/100n)^(10n) but I can't figure out the rate.
    If you are saying find the slope for

    y=P\bigg(1+\bigg(\frac{r}{100n}\bigg)^{10n}\bigg)?

    then the slope in respect to which letter??
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  3. #3
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    Quote Originally Posted by keemariee View Post
    Suppose that we want a certain endowment to pay 50,000 dollars in cash ten years from now. The endowment will be set up today with 5,000 dollars principal and locked in at a fixed interest rate. What interest rate (compounded continuously) is needed to guarantee the desired payoff?

    I know that Amount = P(1+(r/100n)^(10n) but I can't figure out the rate.
    I don't normally do financial mathematics (unless I'm charging like a wounded bull some company or another) but I'll make an exception here.

    You have the wrong formula if the principle is compounded continuously. The correct formula is

    A = A_0 e^{rt}

    where t is the number of years, A is the amount after time t, A_0 is the initial invetsment and r is the annual interest rate.

    Substitute the given values for t, A and A_0 and solve for r.
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