Question

you invest $1300 in an account at interest rate r, compounded continuously. Find the time required for the amount to double and triple. (Round your answers to two decimal places.) r = 0.074

Answer 1

Answer:

• 1. For the amount to double: 9.37 years

• 2. For the amount to triple: 14.85 years

Explanation:

The equation for continuosly compounded interest is:

• $F=P\times e^{rt}$

Where:

• P is the amount that you invest today: $1,300
• F is the value after t years: the double or triple of $1,300
• r is the annual interest rate: 0.074

1. For the amount to double:

Substitute the values and solve for t:

             $2\times \ 1,300=\ 1,300\times e^{0.074t}\\ \\ 0.074t=\ln 2\\ \\ t=\ln 2/0.074=9.37years$

2. For the amount to triple:

            $3\times \ 1,300=\ 1,300\times e^{0.074t}\\ \\ 0.074t=\ln 3\\ \\ t=\ln 3/0.074=14.85years$