Question

Janice has $5,000 invested in a bank that pays 9.4% annually. How long will it take for her funds to triple? 14.31 years 11.86 years 13.70 years 12.23 years 10.64 years

Answer 1

Janice's funds will take approximately 11.86 years to triple.

Step-by-step explanation:

To determine how long it will take for Janice's funds to triple, we can use the formula for compound interest: A = P(1 + r)^t, where A is the final amount, P is the principal amount, r is the interest rate, and t is the time in years. In this case, Janice's initial investment is $5,000 and she wants it to triple, so the final amount is $15,000. The interest rate is 9.4% or 0.094. We need to solve for t, so the equation becomes:

$15,000 = $5,000(1 + 0.094)^t

Divide both sides of the equation by $5,000 to isolate the exponential term:

3 = (1 + 0.094)^t

Next, take the natural logarithm of both sides to eliminate the exponent:

ln(3) = ln((1 + 0.094)^t)

Apply the logarithmic property of exponents to bring down the t:

t * ln(1 + 0.094) = ln(3)

Finally, divide both sides by ln(1 + 0.094) to solve for t:

t = ln(3) / ln(1 + 0.094)

Using a calculator, we find that t is approximately 11.86 years.

Answer 2

It will take approximately 11.86 years for Janice's funds to triple.

Step-by-step explanation:

To determine how long it will take for Janice's funds to triple, we can use the formula for compound interest:

Final amount = Principal amount × (1 + Annual interest rate)Number of years

Let Y be the number of years it takes for her funds to triple:

5000 × (1 + 0.094)Y = 3 × 5000

Dividing both sides by 5000 gives:

(1 + 0.094)Y = 3

Taking the logarithm of both sides:

Y × log(1 + 0.094) = log(3)

Dividing both sides by log(1 + 0.094) gives:

Y = log(3) / log(1 + 0.094)

Using a calculator, we find that Y is approximately 11.86 years.