Final answer:
To calculate the future balance of a $900 investment at 2.25% with daily compounding interest over 50 years, use the compound interest formula A = P(1 + r/n)^(nt). Substituting the given values and solving for A will provide the accumulated amount, showcasing the substantial growth potential through the power of compound interest.
Step-by-step explanation:
Calculating the Future Value of an Investment with Daily Compounding Interest
The question concerns the subject of compound interest, a fundamental concept in financial mathematics. To find the balance after 50 years of investing $900 at a rate of 2.25% with daily compounding, we use the compound interest formula: A = P(1 + r/n)^(nt). Here, A is the amount of money accumulated after n years, including interest. P is the principal amount ($900), r is the annual interest rate (2.25%), n is the number of times that interest is compounded per year (daily, so 365), and t is the time the money is invested for (50 years).
Substituting the given values, we calculate A = $900 (1 + 0.0225/365)^(365*50). After performing the calculations, we'll receive the future value of the investment. This demonstrates the power of compounding, where interest is earned not only on the initial principal but also on the accumulated interest over time.
Understanding these calculations is critical for anyone planning their financial future, as it demonstrates how invested money can grow over time due to the effects of compounding. Starting to save money early and letting compound interest work its magic can lead to substantial growth of your initial investment.