Homework explain

Question

At what rate compounded continuously must money be invested to triple in 6 years?

Answer 1

For compound continuous problems, you would use this formula:

P = P_oe^r(t) P is the ending principle, P_o is the original principle, e is ln 1, r is the annual interest rate, and t is time in years.

3P = P e^r(6) To triple the original principle, use P for both

divide both sides by P

3 = e^6r

take the natural log of both sides

ln 3 = ln e^6r

us the power rule on the right side

ln 3 = 6r ln e ln e = 1, so divide both sides by 6 and get

(ln 3)/6 = r

r = 0.18310204811

18.31% will triple the money invested for 6 years compounded continuously

Answer 2

A = pe^rt

3p = pe^6r

3 = e^6r

ln 3 = 6r

1.098612289 ≈ 6r

0.18≈3102048 ≈ r