Carmen wanted to buy a new motorcycle and put $4,839.00 into an account which earns interest compounded continuously. After 10 months, she withdrew the entire balance of $5,542.00 and bought the motorcycle. What was the interest rate on the account?

To find the interest rate on Carmen's account where she deposited $4,839.00 and withdrew $5,542.00 after 10 months with continuous compounding, we can use the formula for continuous compounding:

A = P * e^(rt)

Where:

- A is the final amount after t time periods

- P is the initial principal amount

- e is Euler's number (approximately 2.71828)

- r is the interest rate

- t is the time in years

Given:

- Initial deposit, P = $4,839.00

- Final amount, A = $5,542.00

- Time, t = 10 months = 10/12 = 0.8333 years

We can rearrange the formula to solve for the interest rate (r):

r = (1/t) * ln(A/P)

Now, plug in the values:

r = (1/0.8333) * ln(5542/4839)

r = 1.2 * ln(1.1455)

r = 1.2 * 0.1395

r = 0.1674 or approximately 16.74%

Hope this helped! :)

sqdancefan sqdancefan · Answer 2 · 2024-04-11T13:00:11-04:00

Answer:

16.3%

Step-by-step explanation:

You want to know the continuously compounded interest rate on an account that grows $4839 to $5542 in 10 months.

Balance

The account balance is given by ...

A = Pe^(rt)

where r is the annual rate, and t is the number of years.

Interest

Solving for r gives ...

A/P = e^(rt)

ln(A/P) = rt

r = ln(A/P)/t

Here we have A=5542, P=4839, t=10/12, so the interest rate is ...

r = ln(5542/4839)/(10/12) ≈ 0.1628 ≈ 16.3%

The interest rate on the account was about 16.3%.