Question

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

Answer 1

Answer:

1 year

Step-by-step 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:

$\displaystyle e^{\left( 1.045\cdot t \right) }=3\\\\1.0.45t=ln(3)\\\\t=\dfrac{ln(3)}{1.045}=1.051304...$

Rounding to the nearest whole number gives 1 year.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you