Final answer:
The balance in Franklin's savings account at the beginning of the third quarter, after depositing $3,420 at a simple interest rate of 3.75%, is approximately $3,484.13, calculated using the simple interest formula over a 0.5-year period.
Step-by-step explanation:
The student has asked about calculating simple interest and determining the account balance after a certain period. In this case, Franklin deposited $3,420 into a savings account with a simple interest rate of 3.75%. To find the balance at the beginning of the third quarter, we need to calculate the interest for half a year (since a quarter is 3 months and the third quarter is from July to September).
The formula for simple interest is: Principal × Interest Rate × Time. Here, the principal is $3,420, the annual interest rate is 3.75%, and the time is 0.5 years.
Interest = $3,420 × 0.0375 × 0.5
Calculating this gives us an interest amount of $64.125. Adding this to the principal amount, we get:
Total balance = Principal + Interest
Total balance = $3,420 + $64.125
Total balance = $3,484.125
Thus, the balance in Franklin's account at the beginning of the third quarter would be approximately $3,484.13, so looking at the options provided, the closest value is option (d) $3,482.10, which seems to be a rounding discrepancy.