Katelyn invested $1500 into her account which earned interest compounded continuously. After 10 years, she discovered that she had $3935.36. What interest rate percent did Katelyn earn? % interest

Given:

Principal = $1500

Time = 10 year

Amount after interest compounded continuously = $3935.36

To find:

The rate of interest.

Solution:

The formula for amount after continuous compound interest is:

Where, P is principal, r is the rate of interest in decimal and t is time in years.

Putting in the above formula, we get

Taking ln on both sides, we get

Divide both sides by 10.

The rate of interest in percentage is:

Therefore, the required rate of interest is 9.645%.