How much simple interest would $800 earn in 300 days in a non-leap year at an interest rate of 1.71%? Round to the nearest cent. A) $12.24 B) $11.24 C) $10.24 D) $9.24
The correct answer and explanation is:
To calculate the simple interest, you can use the formula for simple interest: I=P×r×tI = P \times r \times t
Where:
- II is the interest earned
- PP is the principal amount (initial investment)
- rr is the interest rate (in decimal form)
- tt is the time period in years
Step 1: Identify the values from the problem
- Principal (PP) = $800
- Interest rate (rr) = 1.71% = 0.0171 (convert percentage to decimal)
- Time period (tt) = 300 days
Since the year is non-leap, it has 365 days. To convert 300 days to years: t=300365t = \frac{300}{365}
Step 2: Substitute the values into the formula
I=800×0.0171×300365I = 800 \times 0.0171 \times \frac{300}{365}
Step 3: Perform the calculation
First, calculate the fraction for time: 300365=0.8219\frac{300}{365} = 0.8219
Now calculate the interest: I=800×0.0171×0.8219I = 800 \times 0.0171 \times 0.8219 I=800×0.01404=11.24I = 800 \times 0.01404 = 11.24
Step 4: Round to the nearest cent
The interest earned is $11.24.
Final Answer:
The correct answer is B) $11.24.