Question

Jeremias invested $20 at a rate of 8.5% compounded continuously. How long would it take to triple his money?

Answer 1

Answer:

• 13

Step-by-step explanation:

Use formula for continuous interest:

• A = $Pe^{rt}$, where r- interest rate, t- time in years

If A = 3P, and r = 0.085 then the equation is:

• $3P = Pe^{0.085t}$
• $3 = e^{0.085t}$
• ln 3 = 0.085t
• 1.099 = 0.085t
• t = 1.099 / 0.085
• t = 12.9 ≈ 13 years

Answer 2

The formula for compounded continuously is A = Pe^rt where A if the final amount, P is the initial value, r is the rate and t is the length of time.

E is the constant for continuous interest.

Using the information from the problem $20 tripled would be 20x3 = $60

Now you have 60 = 20e^0.085(t)

We need to solve for t:

Divide both sides by 20:

e^0.085(t) =3

Apply the exponent rule:

0.085(t) = ln(3)

Solve for t:

T = ln(3)/0.085

T = 12.92 years. (Round off as needed)