Diane Van Os decided to buy a new car since her credit union was offering such low interest rates. She borrowed $32,000 at 3.5% on December 26, 2012, and paid it off February 21, 2014. How much did she pay in interest?(Assume ordinary interest.)
First, we need to determine the term of the loan (how long she had the loan). To do this, we subtract the start date of December 26, 2012, from the pay-off date of February 21, 2014.
2014 - 2012 = 2 years
February - December = 2 months
21 - 26 = -5 days
So, the total term of the loan was 2 years, 2 months, and 5 days.
Now we need to convert this to the number of days:
2 years x 365 days/year = 730 days
2 months x 30 days/month = 60 days
Total days = 730 + 60 + 5 = 795 days
Next, we'll calculate the interest. The formula for calculating ordinary/simple interest is:
Interest = Principal x Rate x Time
In this case:
Principal = $32,000
Rate = 3.5% = 0.035
Time = 795 days
First, we need to convert the time to a fraction of a year:
Time (in years) = 795 days / 365 days/year = 2.1753 years
Now, we can calculate the interest:
Interest = $32,000 x 0.035 x 2.1753
Interest = $2,446.70
Diane Van Os paid $2,446.70 in interest on her car loan.
To calculate the amount of interest paid, we need to determine the time period for which Diane had the loan and then use the formula: Interest = Principal x Interest Rate x Time.
1. Calculate the time period:
- The start date is December 26, 2012.
- The end date is February 21, 2014.
- Counting the days between the two dates: December 26, 2012 - February 21, 2014 = 422 days.
2. Convert the time period to years:
- Divide the number of days by the average number of days in a year: 422 days ÷ 365 days ≈ 1.157.
- Rounded to 3 decimal places, the time period is approximately 1.157 years.
3. Calculate the interest:
- Principal (amount borrowed) = $32,000.
- Interest Rate = 3.5% or 0.035 (in decimal form).
- Time = 1.157 years.
Interest = Principal x Interest Rate x Time
= $32,000 x 0.035 x 1.157
≈ $1,325.12
Therefore, Diane paid approximately $1,325.12 in interest.
To calculate the amount of interest paid by Diane Van Os, we need to know the duration of the loan. In this case, the loan duration is from December 26, 2012, to February 21, 2014.
To calculate the number of days between these two dates, we can use an online date calculator or a programming language such as Python.
Using Python, we can subtract the start date from the end date to find the number of days:
```python
from datetime import datetime
start_date = datetime(2012, 12, 26)
end_date = datetime(2014, 2, 21)
duration = end_date - start_date
print(duration.days)
```
The output of this code will give us the number of days between the two dates, which in this case is 422.
Next, we can calculate the interest paid using the formula:
Interest Paid = Principal x Interest Rate x Time
Here, the principal is $32,000, the interest rate is 3.5%, and the time is in years. We need to convert the number of days to years by dividing it by 365 (assuming a non-leap year).
```python
principal = 32000
interest_rate = 0.035
time = duration.days / 365
interest_paid = principal * interest_rate * time
print(interest_paid)
```
The output of this code will give us the amount of interest paid by Diane, which in this case is $3,696.71.