Final answer:
The present value of a $250 payment to be made in three years at a 3% interest rate is approximately $228.78. Option 2, valued at $231, is the closest to this calculated present value. The concept of compound interest involves the calculation of interest on both the initial principal and the accumulated interest.
Step-by-step explanation:
The question asks to determine the present value of a $250 payment that will be made three years in the future given an interest rate of 3 percent. To calculate the present value, we use the formula for finding the present value of a single future payment which is Present Value (PV) = Future Value (FV) / (1 + r)^n, where r is the interest rate and n is the number of periods. Applying the formula, PV = $250 / (1 + 0.03)^3 results in a value of approximately $228.78.
Reviewing the given options, none of them exactly match the calculated present value of $228.78. However, option 2 at $231 is the closest approximation to the correct present value among the given choices. Keep in mind, compound interest involves the calculation of interest on both the initial principal and the accumulated interest from previous periods.
To illustrate further, let's consider the difference between simple interest and compound interest. Simple interest is calculated only on the principal amount of a loan or deposit. In contrast, compound interest includes interest on the interest already earned. For example, the total future amount with simple interest is $115 if you start with $100 at a 5% interest rate for 3 years, as it only applies interest to the initial $100. However, compound interest would result in a higher amount as interest would also be applied to the interest earned in each year.