Final answer:
The student's question is about calculating the future value of daily savings using a compound interest rate over 8 years. Unlike simple interest that only applies to the principal, compound interest is calculated on the principal and the accumulated interest, resulting in a higher total over time.
Step-by-step explanation:
The question involves calculating the future value of a sum of money when compound interest is applied. Afnan has been saving $135.00 daily for the last 8 years at an interest rate of 5.700%, compounded annually. To find the future value with compound interest, you need to use the formula: Future Value = P(1 + r/n)nt, where P is principal, r is annual interest rate, n is the number of times the interest is compounded per year, and t is time in years.
However, since Afnan makes daily contributions, we must use a more complex version of the compound interest formula that accounts for regular contributions. This is typically done using the future value of an annuity formula in combination with the compound interest formula.
Compound interest differs from simple interest in that it is calculated on the initial principal, which also includes all of the accumulated interest from previous periods. An example of simple interest on a $100 investment over 3 years at an annual interest rate of 5% would be calculated as $100 + ($100 × 0.05 × 3) = $115. Whereas compound interest would take the initially invested amount and apply interest to the new total amount each period, leading to a higher total over time.
For example, $1,000 invested at a 2% annual interest rate compounded annually for 5 years would be $1,000(1+0.02)5 = $1,104.08, demonstrating the effect of compounding over time. Compound interest can significantly increase the total amount saved, especially over long periods and with larger sums of money.