Question

Michael put $3500 in an account with continuously compounded interest four years ago. Michael currently has $3946.24 in the account (and he has not made any other deposits ). What is the interest rate for the account? Round to the nearest percent.

Answer 1

To find the interest rate for the account, use the formula for compound interest, A = P e^(rt). Plugging in the values, we find that the interest rate is approximately 2.7%.

Step-by-step explanation:

To find the interest rate for the account, we can use the formula for compound interest: A = P e^(rt), where A is the final amount, P is the principal amount, e is the base of the natural logarithm, r is the interest rate, and t is the time in years. In this case, the principal amount is $3500, the final amount is $3946.24, and the time is 4 years. Plugging these values into the formula, we get:

$3946.24 = $3500 e^(4r)

Dividing both sides of the equation by $3500, we get:

e^(4r) = 1.126928

Taking the natural logarithm of both sides, we get:

4r = ln(1.126928)

Dividing both sides of the equation by 4, we get:

r = ln(1.126928)/4

Using a calculator, we find that the interest rate is approximately 2.7%.