Final answer:
To find the interest earned in the first week, we can use the compound interest formula. The ending balance after one week is the principal amount plus the interest earned. To calculate the balance after one month and the interest earned in the first month, we use the same formula but with the appropriate time and compounding frequency.
Step-by-step explanation:
a. To calculate the interest earned in the first week, we need to use the formula for compound interest: A = P(1 + r/n)^(nt), where:
- A is the ending balance
- P is the principal amount (initial deposit)
- r is the annual interest rate (as a decimal)
- n is the number of compounding periods per year
- t is the number of years
In this case, Rhonda deposited $9,500 with an interest rate of 3 1/4% (0.0325) compounded weekly. So, for the first week (t = 1 week), the interest earned is:
Interest = $9,500 * (1 + 0.0325/52)^(52*1) - $9,500
b. The ending balance after one week (t = 1 week) is the principal amount plus the interest earned:
Ending Balance = $9,500 + Interest
c. To calculate the balance after one month (t = 1 month), we use the same formula, but with t = 4 (4 weeks in a month):
Balance after one month = $9,500 * (1 + 0.0325/52)^(52*4)
d. The interest earned in the first month is the balance after one month minus the principal amount:
Interest earned in the first month = Balance after one month - $9,500