. Ludwig borrowed $8,000 on July 20, at 11% interest. If the loan was due on October 17, what was the amount of interest on the loan using the exact interest method?
To find the amount of interest on a loan using the exact interest method, you need to know the principal amount, the interest rate, and the time period.
Principal amount (P) = $8,000
Interest rate (R) = 11% = 0.11 (in decimal form)
Time period (T) = number of days the loan was outstanding
To determine the time period between July 20 and October 17, we can use the following steps:
Step 1: Determine the number of days in July and count them from July 20 to July 31:
July has 31 days, so the number of days from July 20 to July 31 is 31 - 20 + 1 = 12 days.
Step 2: Determine the number of days in August:
August has 31 days.
Step 3: Determine the number of days in September:
September has 30 days.
Step 4: Determine the number of days in October and count them from October 1 to October 17:
October has 31 days, so the number of days from October 1 to October 17 is 17.
Step 5: Add up the number of days from all the months:
12 + 31 + 30 + 17 = 90 days
The loan was outstanding for 90 days (T = 90).
Now we can calculate the amount of interest using the formula:
Interest (I) = Principal (P) x Rate (R) x Time (T)
I = $8,000 x 0.11 x (90/365)
I = $8,000 x 0.11 x 0.2466
I ≈ $216.96
Therefore, the amount of interest on the loan using the exact interest method is approximately $216.96.
To calculate the exact interest on the loan, we need to know the exact number of days between July 20 and October 17.
Step 1: Calculate the number of days between July 20 and October 17.
July: 31 days
August: 31 days
September: 30 days
October (up to 17th): 17 days
Total number of days = 31 + 31 + 30 + 17 = 109 days
Step 2: Calculate the amount of interest using the exact interest method.
Interest = Principal * Rate * Time
Principal = $8,000
Rate = 11% = 0.11 (in decimal form)
Time = Number of days / Number of days in a year
Number of days in a year = 365 (assuming it is not a leap year)
Time = 109 days / 365 = 0.2986 (approximately)
Interest = $8,000 * 0.11 * 0.2986 = $263.36 (approximately)
Therefore, the amount of interest on the loan using the exact interest method is approximately $263.36.
I = Po*r*t
I = 8000*(0.11/365)*89 = $214.58