Final answer:
The interest rate for a sinking fund to reach $60,000 in 11 years with the same compounding and payment period cannot be directly calculated without the payment amount. Financial calculators or numeric solving methods are needed due to the compounding formula involved. The power of compound interest is significant over time and with larger sums, as indicated by the difference between compound and simple interest outcomes.
Step-by-step explanation:
To calculate the interest rate needed for a sinking fund to reach a specified amount with compounding periods matching the payment periods, we use the future value of an annuity formula:
Future Value = Payment x [(1 + interest rate)number of periods - 1] / interest rate
In this scenario, we need to determine the interest rate that will allow an annuity to reach $60,000 in 11 years with regular annual payments. Since the exact payment amount is not provided, we cannot compute the interest rate directly. Generally, you would use financial calculators or software capable of solving for the interest rate in such a formula, which typically requires iterative methods or numerical solutions because of the compounding nature of the equation.
It is important to note the power of compound interest over simple interest, especially over long periods and with larger sums. As given in the reference information, a three-year scenario shows that compound interest yields $115.76, which is higher than what is obtained with simple interest, due to the interest on the accumulated interest.