Final answer:
The balance of a bank account with a $500 initial deposit and a 0.5% monthly interest rate at the end of one year would be approximately $503.09.
Step-by-step explanation:
To calculate the balance of a bank account with monthly interest, we utilize the compound interest formula rather than the simple interest formula outlined in the given examples.
Starting with an initial deposit of $500 in an account with a monthly interest rate of 0.5%, and assuming there are no additional deposits or withdrawals for one year, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time in years.
So for our calculation:
- P = $500
- r = 0.5% per month, which is 0.005 in decimal.
- n = 12 (since interest is compounded monthly)
- t = 1 (since we are calculating for one year)
The formula becomes:
A = $500(1 + 0.005/12)^(12*1)
After doing the math:
A = $500(1 + 0.00041667)^(12)
A = $500(1.00041667)^(12)
A = $500 * 1.00617 (approximately)
A = $503.09
The balance at the end of one year would be approximately $503.09.