Final answer:
To find out the interest earned by Gwen, we need to determine the initial deposit and subtract it from the final amount of $3,000.00. The initial deposit is calculated using the formula for compound interest and rearranging it to solve for the principal. Once the principal is found, it is deducted from the final amount to get the total interest earned.
Step-by-step explanation:
To calculate how much interest Gwen earned, we need to find the initial deposit (principal) that grew to $3,000.00 after 2 years with a 1% monthly compounded interest. The formula for compounded interest is A = P(1 + r/n)^(nt), where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for, in years.
In Gwen's case, A is $3,000.00, r is 0.01 (1% expressed as a decimal), n is 12 (since interest is compounded monthly), and t is 2. We rearrange the formula to solve for P:
P = A / (1 + r/n)^(nt)
Substituting the given values, we get:
P = $3,000.00 / (1 + 0.01/12)^(12*2)
After calculating P, the interest Gwen earned can be found by subtracting P from $3,000.00, which is A (the final amount).