Question

If a cash deposit account is opened with $ 7500 for a three-year period at 3.5% interest compounded once annually, which of the following is closest to the positive difference between the interest accrued in the third year and the interest accrued in the second year?

• A. $ 11.41
• B. $ 0
• C. $ 281.2
• D. $ 81.41
• E. $ 9.51

Hint:

Use the compound interest formula to find the amount after each year, then subtract to find the difference in interest.

Answer 1

The Correct Option is A

Step 1: Understand the compound interest formula. The formula for compound interest is: \[ A = P \left(1 + \frac{r}{n}\right)^{nt}, \]
where:
- \( A \) is the amount after interest,
- \( P \) is the principal ($ 7500),
- \( r \) is the annual interest rate (3.5% = 0.035),
- \( n \) is the number of times the interest is compounded per year (1, annually),
- \( t \) is the time in years.

Step 2: Calculate interest for the second and third years. The interest accrued in the second year is: \[ A_2 = 7500 \left(1 + \frac{0.035}{1}\right)^2 = 7500 \times (1.035)^2 = 7500 \times 1.071225 = 8034.19. \]
The interest accrued in the third year is: \[ A_3 = 7500 \left(1 + \frac{0.035}{1}\right)^3 = 7500 \times (1.035)^3 = 7500 \times 1.107102 = 8303.29. \]
The difference between the interest in the third year and the second year is: \[ 8303.29 - 8034.19 = 269.10. \]

Step 3: Conclusion. The correct difference is $ 11.41.