Calculating Account Balance and Interest Rate: A Reflective Perspective

How can we calculate the balance of a bank account at the end of one year with monthly interest?

a. (500) * (1.005)¹² or $530.84

b. About 6.17%, because (1.005) 12 is about 1.0617.

Answer:

The balance at the end of one year would be $530.84 and the effective annual interest rate would be about 6.17%.

Reflecting on the process of calculating the balance and interest rate of a bank account with monthly interest can provide valuable insights into personal finance management. By understanding the formula and steps involved, individuals can make informed decisions about their savings and investments.

To calculate the balance of the account at the end of one year, we can use the formula: Ending Balance = Principal * (1 + Interest Rate)^Time Period. In this case, the principal amount is $500, the interest rate is 0.5% (or 0.005 as a decimal), and the time period is 12 months.

Plugging these values into the formula, we get: Ending Balance = $500 * (1 + 0.005)^12 = $530.84. This means that if $500 is put into the account, the balance would grow to $530.84 at the end of one year, assuming no additional deposits or withdrawals are made.

The effective annual interest rate can be calculated using the formula: Effective Annual Rate = (1 + Monthly Rate)^Number of Months - 1. Plugging in the values, we get: Effective Annual Rate = (1 + 0.005)^12 - 1 = 0.0617 or 6.17%.

Understanding the concepts of compound interest and annualized rates can empower individuals to make informed financial decisions and optimize their savings over time. By reflecting on the process of calculating account balances and interest rates, one can develop a deeper appreciation for the impact of interest on wealth accumulation.