Final answer:
To find the size of Timothy's periodic deposits, the future value of an annuity formula is needed, considering the quarterly deposit frequency and monthly compound interest over 24 years. Compound interest greatly affects the growth of investments over time, as it builds on both the principal and accumulated interest.
Step-by-step explanation:
The student is asking to determine the size of the equal deposits made into a retirement fund that has grown due to compound interest. To do this, one would use the future value of an annuity formula which is well-suited for situations where deposits are made at regular intervals and interest is compounded. Since the fund has been accumulating at a rate of 3.65% compounded monthly for 24 years, and the deposits are made quarterly, we need to account for this frequency of compounding and deposits when applying the formula. By doing so, we can calculate the amount of each payment that would lead to the accumulated $50,000.
Compound interest has a significantly greater impact on the growth of investments than simple interest, as it takes into account the interest on both the initial principal and the accumulated interest over time. This is seen in the example where a small amount of money grows more than it would under simple interest due to the effect of compounding. In Timothy's case, the significant growth of his retirement fund over a long period of 24 years illustrates the power of compound interest. Ultimately, the exact size of Timothy's regular deposits can be determined through financial calculations that factor in the interest rate, compounding frequency, and the number of periods for the investment.