Question

How long will it take $8000 to grow to $40,000 if it is invested at 5% APR compounded continuously? Show your work.

less than 25 years

between 25 and 50 years

more than 50 years

Answer 1

Use A = Pe^{rt}. Here 40000 = 8000 e^{0.05t} so 5 = e^{0.05t}.
Take logs: ln 5 = 0.05 t, hence t = ln 5 / 0.05 = 20 ln 5 ≈ 32.19 years.

So it takes about 32.2 years — between 25 and 50 years.