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?
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 125 years.
Step 2: Calculate the Interest Earned
Using the formula for simple interest I=P⋅r⋅t, where:
P=458.93
r=0.053
t=125
The interest earned is calculated as follows:
I=458.93⋅0.053⋅125≈10.1347
Step 3: Calculate the Total Amount in the Account
The total amount in the account on July 1 is given by:
Total Amount=Initial Balance+Interest Earned+Deposit
Substituting the values:
Total Amount=458.93+10.1347+321.27≈790.3347
Final Answer
The amount in your account on July 1, after your deposit, is approximately \\(\boxed{790.3347}\\).