Final answer:
The total value difference between a simple interest account and a compound interest account for a $5,500 deposit over 25 years at 4.1% is calculated by finding the total value for each interest type and then subtracting the simple interest total from the compound interest total.
Step-by-step explanation:
The student is asking about the difference in total value between two types of interest calculations: simple interest and compound interest for a deposit of $5,500 over a period of 25 years at an annual interest rate of 4.1%. To calculate the simple interest over 25 years, we use the formula Simple Interest = Principal × Interest Rate × Time. For the compound interest, the calculation is a bit more complex as it involves interest on the initial amount plus the interest accrued over time, which is usually calculated annually in this context.
Using the simple interest formula, our calculation would be: $5,500 × 0.041 × 25 = $5,637.5 in simple interest. Adding this to the initial deposit, the total value would be $11,137.50. For compound interest, we use the formula Total Value = Principal × (1 + Interest Rate)Number of Years. This equals $5,500 × (1 + 0.041)25. After calculating and rounding to the nearest whole number, we can determine the total amount.
Finally, to find the difference in total value between the two interest types, we subtract the total value of the simple interest account from that of the compound interest account.