Final answer:
We use the formulas for simple and compound interest to find how much more could have been earned over 13 years by calculating the future values with each method and subtracting the simple interest total from the compound interest total.
Step-by-step explanation:
The student has presented a problem regarding the calculation of compound interest compared to simple interest over a period of 13 years. To solve this, we will calculate the future amount with simple interest and then with compound interest and find the difference between the two. The formula for simple interest is Principal x Rate x Time and for compound interest, it is Principal x (1 + Rate)^Time.
To calculate the total amount with simple interest, we use the formula: Principal + (Principal x Rate x Time). So, for a $12,500 investment at 5.75% interest over 13 years, the future value with simple interest would be $12,500 + ($12,500 x 0.0575 x 13).
Next, we will use the compound interest formula: Principal x (1 + Rate)^Time. So, the future value with compound interest is $12,500 x (1 + 0.0575)^13.
By finding the difference between these two amounts, we can determine how much more could have been earned if the interest had compounded annually instead of being calculated using simple interest.