Simple Interest with Minimum Monthly Balance: At the beginning of March, Ryan has $621 in his savings account and on 10 March he deposits an additional $60. The bank pays 8% per annum simple interest, credited monthly, and calculates interest on the minimum monthly balance. How much interest does Ryan earn for March (in $)?

Introduction / Context:
This question shows how some banks calculate interest on savings accounts using simple interest and the minimum monthly balance method. The interest is credited monthly, but the rate is annual. You must identify the minimum balance during the month and then compute one month's simple interest on that amount.

Given Data / Assumptions:

• Initial balance on 1 March = $621.
• Additional deposit on 10 March = $60, so balance becomes $681 after that date.
• Annual simple interest rate r = 8% per annum.
• Interest is calculated on the minimum monthly balance.
• Interest is credited monthly, i.e., for one month at a time.

Concept / Approach:
Under the minimum monthly balance method, the bank pays interest on the lowest balance in that month, regardless of later deposits that may raise the balance. Because Ryan starts with $621 and later adds $60 (raising the balance), the minimum balance is $621. Monthly interest is computed using simple interest for t = 1 / 12 year on this minimum balance at the annual rate of 8%.

Step-by-Step Solution:
Step 1: Identify the minimum balance for March. From 1 March until 9 March, balance is $621. From 10 March onwards, balance is $681. Step 2: The minimum balance during the month is therefore $621. Step 3: Annual simple interest rate r = 8% per annum. Step 4: Time for one month t = 1 / 12 year. Step 5: Use SI formula I = (P * r * t) / 100 with P = 621. Step 6: I = (621 * 8 * (1 / 12)) / 100 = (621 * 8) / (12 * 100). Step 7: First compute 621 * 8 = 4,968. Step 8: Now divide by 12 * 100 = 1,200: I = 4,968 / 1,200 ≈ $4.14. Step 9: Therefore, Ryan earns approximately $4.14 interest for March.

Verification / Alternative check:
You can think of the annual interest on $621 at 8% as (621 * 8) / 100 = $49.68. For one month, that is roughly 49.68 / 12 ≈ $4.14. This matches the earlier calculation and confirms that the answer is consistent.

Why Other Options Are Wrong:

• $2.14 and $3.14: Both are too small and would correspond to a lower annual rate or a shorter time period.
• $5.14: Slightly larger than the correct value and does not match 8% per annum for one month.
• $4.80: Corresponds to a higher effective rate or a larger minimum balance than $621.

Common Pitfalls:
Students often mistakenly calculate interest on the highest balance ($681) instead of the minimum balance. Others forget to convert the annual rate to a monthly period and directly use 8% as if it were the monthly rate. Always read the bank's interest calculation rule carefully and adjust the time and balance accordingly.

Final Answer:
The interest Ryan earns for March is $4.14.