Final answer:
The student is interested in determining how much interest Leslie earned on a bank account that had a 13% interest rate compounded annually over 7 years and currently has $800. To answer this, the formula for compound interest should be applied, and after finding the original deposit amount, the earned interest can be calculated by subtracting the deposit from the current amount.
Step-by-step explanation:
The student is asking about the calculation of compound interest from a bank account assuming a certain annual interest rate. The student poses that Leslie deposited some money after winning the lottery and placed the amount in a bank account with a 13% annual interest rate. After 7 years, Leslie has $800 in the account. We need to determine the initial deposit amount (or principal) and calculate the interest earned.
To solve this, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time in years. Since the account compounds annually, n is 1. Rearrange the formula to solve for P. In this case, A = $800, r = 0.13, and t = 7 years.
Substituting the known values and solving for P will give us the initial amount Leslie deposited. After finding P, we can determine the interest earned by subtracting P from A.