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If $14,000 is invested in an account earning 4.5% interest compounded continuously, determine how long it will take the money to triple. Round up to the nearest year.

User Garret
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Final answer:

To determine how long it will take for an investment of $14,000 to triple at an interest rate of 4.5% compounded continuously, you can use the formula for continuous compound interest. It will take approximately 23 years for the money to triple.

Step-by-step explanation:

To determine how long it will take for an investment of $14,000 to triple at an interest rate of 4.5% compounded continuously, we can use the formula for continuous compound interest:

A = P * e^(rt)

Where A is the final amount, P is the principal (initial investment), e is Euler's number (approximately 2.71828), r is the interest rate, and t is the time in years.

In this case, we want the final amount to be triple the principal, so A = 3P. Substituting the values into the formula, we get:

3P = P * e^(0.045t)

Dividing both sides by P, we can cancel out the P's:

3 = e^(0.045t)

To solve for t, we need to isolate the exponent. Taking the natural logarithm (ln) of both sides:

ln(3) = ln(e^(0.045t))

Using the property of logarithms that ln(e^x) = x, we get:

ln(3) = 0.045t

Finally, dividing both sides by 0.045, we find:

t = ln(3) / 0.045 ≈ 22.47

Therefore, it will take approximately 23 years for the money to triple, rounding up to the nearest year.

User Varvara
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