Final answer:
The student's question is about calculating the future value of a $30,000 investment over three years with various compounding frequencies using the compound interest formula. Each frequency daily, monthly, annually, and quarterly will yield a different future value, demonstrating the effects of compounding on the investment's growth.
Step-by-step explanation:
The student is asking for the future value of a $30,000 investment compounded at different frequencies over a period of three years at a rate of 5%. To solve this problem, we can employ the compound interest formula: A = P(1 + r/n)^(nt), where A is the future value of the investment/loan, including interest; P is the principal investment amount (initial deposit or loan amount); r is the annual interest rate (decimal); n is the number of times that interest is compounded per year; and t is the number of years the money is invested or borrowed for.
Calculating for each compounding frequency:
Daily compounding (n = 365): A = $30,000(1 + 0.05/365)^(365*3)Monthly compounding (n = 12): A = $30,000(1 + 0.05/12)^(12*3)Annually compounding (n = 1): A = $30,000(1 + 0.05/1)^(1*3)Quarterly compounding (n = 4): A = $30,000(1 + 0.05/4)^(4*3)
Each calculation will yield a slightly different future value due to the frequency of compounding. For instance, daily compounding will generate more interest than monthly compounding, which in turn generates more interest than annual compounding. The difference in the end amounts illustrates the impact of compounding frequency on the growth of investment, showing how compound interest can make a significant difference over time.