The correct answer is a) Quarterly: 0.07/4, Monthly: 0.07/12, Annually: 0.07.
Here's why:
We need to represent the interest rate in the compound interest formula as the rate divided by the number of compounding periods per year. This way, we're applying the appropriate amount of interest for every compounding period.
So if the interest is compounded quarterly, we divide the annual interest rate by 4. This is because there are four quarters in a year and interest is applied at the end of each quarter. So for this situation it would be 0.07/4.
If the interest is compounded monthly, we'd divide the annual interest rate by 12 for each of the twelve months of the year. Therefore with monthly compounding, we'd write it as 0.07/12.
When interest is compounded annually, we don't need to divide the annual rate of 0.07 at all, because there's only one compounding period in a year—the end of the year. Hence, for yearly compounding, the rate is just 0.07.
So, the interest rate for quarterly, monthly, and annual compounding is represented in the compound interest formula as 0.07/4, 0.07/12, and 0.07 respectively.