Question

Walter invests $100,000 in an account that compounds interest continuously and earns 12%. How long will it take for his money to triple? Round to the nearest tenth of a year.

Answer 1

Answer:

$300000= 100000 e^{0.12 t}$

We divide both sides by 100000 and we got:

$3 = e^{0.12 t}$

Now we can apply natural logs on both sides;

$ln(3) = 0.12 t$

And then the value of t would be:

$t = \frac{ln(3)}{0.12}= 9.16 years$

And rounded to the nearest tenth would be 9.2 years.

Step-by-step explanation:

For this case since we know that the interest is compounded continuously, then we can use the following formula:

$A =P e^{rt}$

Where A is the future value, P the present value , r the rate of interest in fraction and t the number of years.

For this case we know that P = 100000 and r =0.12 we want to triplicate this amount and that means $A= 300000$ and we want to find the value for t.

$300000= 100000 e^{0.12 t}$

We divide both sides by 100000 and we got:

$3 = e^{0.12 t}$

Now we can apply natural logs on both sides;

$ln(3) = 0.12 t$

And then the value of t would be:

$t = \frac{ln(3)}{0.12}= 9.16 years$

And rounded to the nearest tenth would be 9.2 years.