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wolverine [178]
3 years ago
9

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 conti

nuously
Mathematics
2 answers:
quester [9]3 years ago
6 0

Answer:

It should take roughly 3.5 years

Step-by-step explanation:


enyata [817]3 years ago
5 0

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.

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