Question

Danielle deposited $300.00 into a new savings account that earns interest compounded continuously. After 8 years, the balance in the account

was $907.00. What was the interest rate on the account?
O 13.8%
O 12.5%
O 14.5%
O 10.1%

Answer 1

To find the interest rate on the account, we can use the formula for continuous compounding: A = P * e^(rt), where A is the final amount, P is the initial deposit, r is the interest rate, t is the time in years, and e is the base of the natural logarithm (approximately 2.718).

In this case, A = $907, P = $300, and t = 8 years. We need to find r.

907 = 300 * e^(8r)

Now, we'll solve for r:

(907/300) = e^(8r)

3.0233 = e^(8r)

To isolate r, take the natural logarithm of both sides:

ln(3.0233) = 8r

Now, divide by 8:

(ln(3.0233))/8 = r

r ≈ 0.125

To express the interest rate as a percentage, multiply by 100:

0.125 * 100 = 12.5%

So, the interest rate on the account is approximately 12.5%.