Final answer:
By keeping $100 in a bank account with an 8% interest rate when inflation is 4%, you actually gain $4 in purchasing power after one year. This is calculated by subtracting the inflation rate from the nominal interest rate to get the real rate of return.
Step-by-step explanation:
If your savings account pays 8 percent per year, this means that for every $100 you save, it will grow to $108 after one year. However, if prices increase by 4 percent per year due to inflation, the actual purchasing power of your money also changes. To understand how much you actually gain, you need to consider the real rate of return, which accounts for inflation.
The real rate of return is the nominal interest rate (the 8 percent you receive from the bank) minus the inflation rate. In this case, it's 8% - 4% = 4%. Therefore, for every $100 in your savings account, the real gain after one year is 4% of $100, which is $4. So, when you factor in inflation, by keeping $100 in the bank for a year, you actually gain $4 in terms of purchasing power.
To further illustrate, the money grows to $108 nominally, but because inflation is 4%, the $100 you originally had would need to be $104 in one year to keep the same purchasing power. Thus, your actual gains in terms of real value or purchasing power are the difference between $108 and $104, which is again, $4.