Question

Ariana is going to invest $62,000 and leave it in an account for 20 years. Assuming

the interest is compounded continuously, what interest rate, to the nearest tenth of a
percent, would be required in order for Ariana to end up with $233,000?

Answer 1

To find the interest rate required for Ariana to end up with $233,000 after 20 years of continuous compounding, we can use the formula for compound interest. Plugging in the values and solving for the interest rate, we find that Ariana would need an interest rate of approximately 8.9%.

Step-by-step explanation:

To find the interest rate required in order for Ariana to end up with $233,000 after 20 years of continuous compounding, we can use the formula for compound interest:

A = P*e^(rt)

Where:

• A is the final amount ($233,000)
• P is the principal amount ($62,000)
• r is the interest rate (which we are trying to find)
• t is the time in years (20)
• e is Euler's number (approximately 2.71828)

Plugging in the values, we have:

$233,000 = $62,000 * e^(20r)

Divide both sides by $62,000:

e^(20r) = 3.75806

Now take the natural logarithm of both sides:

ln(e^(20r)) = ln(3.75806)

By the property of logarithms, the exponent can be brought down:

20r * ln(e) = ln(3.75806)

Since ln(e) = 1, we have:

20r = ln(3.75806)

Divide both sides by 20:

r = ln(3.75806)/20

Using a calculator, we find that r ≈ 0.0888

Therefore, Ariana would need an interest rate of approximately 8.9% to end up with $233,000 after 20 years of continuous compounding.