Asked by y
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.
All Answers 1
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).
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).
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.