Question

How many years will it take 7000 to grow to 12000 if it is invested at 3.50 compounded​ continuously?

A. 8.93 years
B. 9.76 years
C. 10.42 years
D. 11.18 years

Answer 1

To find the number of years it will take for $7000 to grow to $12000 when invested at a continuous compound interest rate of 3.50%, we can use the formula: A = P * e^(rt). By substituting the values into the formula and solving for t, we find that it will take approximately 9.7557 years for $7000 to grow to $12000.

Step-by-step explanation:

To find the number of years it will take for $7000 to grow to $12000 when invested at a continuous compound interest rate of 3.50%, we can use the formula:

A = P * e^(rt)

Where:

• A is the final amount (which is $12000)
• P is the initial principal (which is $7000)
• r is the continuous interest rate (which is 3.50% or 0.035 in decimal form)
• t is the number of years

By substituting the values into the formula, we get:

$12000 = $7000 * e^(0.035t)

To solve for t, we need to isolate it. Divide both sides of the equation by $7000:

e^(0.035t) = $12000 / $7000

Simplify the right side:

e^(0.035t) = 1.7143

To isolate t, we need to take the natural logarithm of both sides:

ln(e^(0.035t)) = ln(1.7143)

Using the property of logarithms, the exponent comes down as a coefficient:

0.035t * ln(e) = ln(1.7143)

ln(e) is equal to 1, so the equation becomes:

0.035t = ln(1.7143)

To solve for t, divide both sides by 0.035:

t = ln(1.7143) / 0.035

Using a calculator or computer program, we find that t is approximately 9.7557 years.