Question

How many years (approximately) will it take $6,000 to amount $8,000 if it is invested at an annual rate of 9.0% compounded continuously

Answer 1

Answer:

It should take roughly 3.5 years

Step-by-step explanation:

Answer 2

Answer:

3.2 years.

Step-by-step explanation:

We are asked to find the number of years it will take an amount of $6,000 to be $8,000 compounded continuously at an annual rate of 9%.

We will use continuous compound interest formula to solve our given problem.

$A=Pe^{rt}$, where,

A = Amount after t years,

P = Principal amount,

e = Mathematical constant,

r = Interest rate in decimal form,

t = Time in years.

$\ 8,000=\ 6,000e^{0.09*t}$

$\frac{\ 8,000}{\ 6,000}=\frac{\ 6,000e^{0.09*t}}{\ 6,000}$

$\frac{4}{3}=e^{0.09*t}$

Switch the sides:

$e^{0.09*t}=\frac{4}{3}$

Now, we will take natural log of both sides.

$\text{ln}(e^{0.09*t})=\text{ln}(\frac{4}{3})$

$0.09*t=\text{ln}(\frac{4}{3})$

$0.09*t=0.2876820724517808$

$\frac{0.09*t}{0.09}=\frac{0.2876820724517808}{0.9}$

$t=3.19646747\approx 3.2$

Therefore, it take approximately 3.2 years for the amount of $6,000 to be $8,000.