Question

Henry is investing at a continuously compounded annual interest rate of 4.5%. How many years will it take for the balance

to triple? Round your answer up to the nearest whole number, and do not include the units in your answer.

Answer 1

25

Explanation:

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Answer 2

1 year

Explanation:

Hello,

Continuously compounding with an annual interest rate of 4.5% means multiplying the initial investment by (for t tears).

`\displaystyle e^((1+4.5\%)t)=e^(\left( 1.045\cdot t \right) )`

So we need to find t so that:

`\displaystyle e^(\left( 1.045\cdot t \right) )=3\\\\1.0.45t=ln(3)\\\\t=(ln(3))/(1.045)=1.051304...`

Rounding to the nearest whole number gives 1 year.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you