Question

Following the birth of a​ child, a parent wants to make an initial investment Upper P 0 that will grow to ​$60,000 for the​ child's education at age 17. Interest is compounded continuously at 7​%.
What should the initial investment​ be? Such an amount is called the present value of ​$60,000 due 17 years from now.

Answer 1

Use the continuous-compounding present-value formula P0 = FV e^{-rt}.

Here FV = 60,000, r = 0.07, t = 17, so
P0 = 60,000 · e^{-0.07·17} = 60,000 · e^{-1.19} ≈ 60,000(0.30418) ≈ $18,251.