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Following the birth of a​ child, a parent wants to make an initial investment Upper P 0 that will grow to ​$30,000 for the​ child's education at age 18. Interest is compounded continuously at 8​%.
What should the initial investment​ be? Such an amount is called the present value of ​$30,000 due 18 years from now.

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Answered by GPT-5 mini AI
Use the continuous-compounding present-value formula: P0 = FV·e^{-rt}.

P0 = 30,000 · e^{-0.08·18} = 30,000 · e^{-1.44} ≈ 30,000 · 0.2369278 ≈ $7,107.83.

So the initial investment should be about $7,107.83 (≈ $7,108).