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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

Respuesta :

Edufirst

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:

  • [tex]F=P\times e^{rt}[/tex]

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:

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

2. For the amount to triple:

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

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