A bank pays interest to its customers on the last day of the year. The interest paid to a custormer is calculated as 10% of the average monthly balance maintained by the customer. John is a customer at the bank. On the last day, when the interest was accumulated into his account, his bank balance doubled to $5680. What is the average monthly balance maintained by John in his account during the year?

Options

A. `2840`
B. `5680`
C. `6840`
D. `28400`

Answer

To find the average monthly balance maintained by John in his bank account during the year, we can follow these steps:

### Step 1: Determine the bank balance before interest accumulation
According to the problem, John's bank balance doubled to $5680 after the interest was added. Therefore, we can find the balance before the interest was added by dividing $5680 by 2.

\[ \text{Balance before interest} = \frac{5680}{2} = 2840 \]

### Step 2: Calculate the interest amount
The interest amount is the difference between the bank balance after interest and the balance before interest. Thus, we can calculate the interest amount as follows:

\[ \text{Interest amount} = 5680 - 2840 = 2840 \]

### Step 3: Set up the equation for average monthly balance
The interest paid to a customer is calculated as 10% of the average monthly balance maintained by the customer. We can express this mathematically as:

\[ 0.10 \times \text{Average Monthly Balance} = \text{Interest Amount} \]

Substituting the interest amount we calculated:

\[ 0.10 \times \text{Average Monthly Balance} = 2840 \]

### Step 4: Solve for the average monthly balance
To find the average monthly balance, we can rearrange the equation:

\[ \text{Average Monthly Balance} = \frac{2840}{0.10} \]

Calculating this gives:

\[ \text{Average Monthly Balance} = 2840 \times 10 = 28400 \]

### Conclusion
Thus, the average monthly balance maintained by John in his account during the year is:

\[ \text{Average Monthly Balance} = 28400 \]