Question

Joshua is going to invest $9,000 and leave it in an account for 5 years. Assuming the interest is compounded continuously, what interest rate, to the nearest tenth of a percent, would be required in order for Joshua to end up with $12,500?

Answer 1

To find the interest rate required for Joshua to end up with $12,500 in 5 years with continuous compound interest, we can use the formula A = P*e^(rt). Plugging in the given values and solving for r, we find that the interest rate required is approximately 4.54%.

Step-by-step explanation:

To find the interest rate required for Joshua to end up with $12,500, 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), r is the interest rate, and t is the time in years.

Plugging in the given values: $12,500 = $9,000 * e^(r*5)

Dividing both sides by $9,000, we get: 1.3889 = e^(5r)

Now, we can take the natural logarithm of both sides: ln(1.3889) = ln(e^(5r))

Using the logarithm property, ln(e^(5r)) = 5r * ln(e) = 5r * 1 = 5r

So, ln(1.3889) = 5r

Dividing both sides by 5, we find that the interest rate required is approximately 0.0454, or 4.54%.