Final answer:
Interest on a $17,000 investment over 25 years can be calculated using specific formulas for simple and compound interest. The total interest varies depending on the compounding frequency, demonstrating the substantial benefits of compound interest over time.
Step-by-step explanation:
To calculate the total interest earned on a $17,000 investment over 25 years with various interest compounding schedules, we use different formulas for simple interest and compound interest. Here are the calculations:
Simple interest: Interest = Principal x Rate x Time. So, the total simple interest would be $17,000 x 0.07 x 25 = $29,750.
Compounded annually: The formula for compound interest is A = P(1 + r/n)^(nt). For annually compounded interest, n = 1, so the formula simplifies to A = $17,000(1 + 0.07)^25. The total interest would then be A - P, where P is the principal amount.
Compounded quarterly: When compounded quarterly, n = 4. The new total would be A = $17,000(1 + 0.07/4)^(4*25). Again, the total interest is A - P.
Compounded monthly: Compounded monthly means n = 12. So the total would be A = $17,000(1 + 0.07/12)^(12*25), and the total interest is A - P.
As seen in the provided example, over a short period of time and with smaller amounts, the difference between simple and compound interest may seem minor. However, over a longer period and with larger investments, such as $17,000 over 25 years, the power of compound interest is significant, resulting in a substantial increase in the total interest earned.