Final answer:
To find the equivalent simple interest rate, we must calculate the total compound interest over the two-year period and then apply the simple interest formula to solve for the rate that would yield the same amount of interest.
Step-by-step explanation:
To calculate the equivalent simple interest rate for the 2% compound interest per month over two years, we first need to determine the overall compound interest for the period.
Compound interest is calculated using the formula A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the time the money is invested for in years. Here, we are compounding monthly (n = 12), the annual interest rate is 24% since it's 2% per month (r = 0.24), and the time is 2 years (t = 2).
First, we find the A, the total accumulated amount after 2 years, and then we find the total compound interest by subtracting the principal from A.
Then to find the equivalent simple interest rate, we use the simple interest formula I = P * r * t, where I is the interest, P is the principal, r is the rate of interest per period, and t is the time the money is invested for in periods. We calculate this for the total amount of compound interest earned over the 2 years (which is our 'I' in this scenario), keeping the same principal P and period t, and solve for the rate r.
Finally, we multiply r by 100 to express it as a percentage. This yields the equivalent simple interest rate for the 2-year period.