Final answer:
The compound interest on $2,500 at a rate of 6.75% compounded daily for 20 days is approximately $8.76, calculated using the compound interest formula, making the correct answer (b).
Step-by-step explanation:
The compound interest on $2,500 at 6.75% compounded daily for 20 days can be calculated using the compound interest formula:
Compound Interest = Principal × ( (1 + ((Rate) / ((Number of Compounding Periods per Year))) ⁴ × × (Total Number of Compounding Periods) - Principal
To answer this question, we assume the year has 365 days which is commonly used for financial calculations making the number of compounding periods per year 365. Therefore, the total number of compounding periods would be 20.
Plugging in the numbers:
- Principal ($P) = $2,500
- Rate (r) = 6.75% or 0.0675 as a decimal
- Number of Compounding Periods per Year (n) = 365
- Total Number of Compounding Periods (t) = 20
Compound Interest = 2,500 × ( (1 + (0.0675 / 365))^ × (20/365) - 2,500
It is important to remember that financial calculators and spreadsheet programs are very useful for these types of calculations due to the daily compounding.
After calculating, we find that the compound interest earned is approximately $8.76, which means the correct answer is option (b).