Questions: On February 1, the balance in your account is 458.93. On July 1, you deposit 321.27. Your bank pays 5.3% interest that is calculated on the last day of the month. What is the amount in your account on July 1, after your deposit?

On February 1, the balance in your account is 458.93. On July 1, you deposit 321.27. Your bank pays 5.3% interest that is calculated on the last day of the month. What is the amount in your account on July 1, after your deposit?

Transcript text: On February 1, the balance in your account is $\$ 458.93$. On July 1, you deposit $\$ 321.27$. Your bank pays $5.3 \%$ interest that is calculated on the last day of the month. What is the amount in your account on July 1, after your deposit?

Solution

Solution Steps

To solve this problem, we need to calculate the simple interest earned from February 1 to June 30 (5 months) on the initial balance of $458.93. The interest rate is 5.3% per annum, so we will adjust it for the 5-month period. After calculating the interest, we will add it to the initial balance and then add the deposit made on July 1 to find the total amount in the account.

Step 1: Calculate the Time Period

The time period from February 1 to June 30 is $ \frac{5}{12} $ years.

Step 2: Calculate the Interest Earned

Using the formula for simple interest $ I = P \cdot r \cdot t $, where:

$ P = 458.93 $
$ r = 0.053 $
$ t = \frac{5}{12} $

The interest earned is calculated as follows: \[ I = 458.93 \cdot 0.053 \cdot \frac{5}{12} \approx 10.1347 \]

Step 3: Calculate the Total Amount in the Account

The total amount in the account on July 1 is given by: \[ \text{Total Amount} = \text{Initial Balance} + \text{Interest Earned} + \text{Deposit} \] Substituting the values: \[ \text{Total Amount} = 458.93 + 10.1347 + 321.27 \approx 790.3347 \]