Alicia borrowed $8,500 at 6% ordinary interest for 180 days. After 40 days, she made a partial payment of $2,000. After another 70 days, Alicia made a second partial payment of $2,000. What is the final amount due on the loan?
P = Po + Po*r*t
P = 8,500 + 8500*(0.06/360)*40 - 2000 = $8556.67 - 2000 = $6556.67 After 40 days.
P = 6556.67 + 6556.67*(0.06/360)*70 - 2000 = 6633.16 - 2000 = 4633.16 After 70
days.
P = 4633.16 + 4633.16*(.0/360)*(180-110)= $4687.21 After 180 days.
Well, Alicia certainly knows how to keep us on the edge of our seats with her partial payments! Let's see how the math circus unfolds.
First, let's calculate the interest for the initial 40 days. Alicia borrowed $8,500, and the interest rate is 6%. So, for 40 days, the interest would be $8,500 * 0.06 * (40/365) = $70.41.
After the first partial payment of $2,000, the remaining balance is $8,500 - $2,000 = $6,500. But wait, the show isn't over yet!
Now let's calculate the interest for the next 70 days. The remaining balance is $6,500, and the interest rate and time period remain the same. So, the interest for the next 70 days would be $6,500 * 0.06 * (70/365) = $86.85.
After the second partial payment of $2,000, the remaining balance is $6,500 - $2,000 = $4,500. And now, ladies and gentlemen...
To find the final amount due on the loan, we need to calculate the interest for the remaining 70 days. The remaining balance is $4,500, and the interest rate and time period remain the same. So, the interest for the final 70 days would be $4,500 * 0.06 * (70/365) = $55.07.
Now, let's add up all the interest: $70.41 (40 days) + $86.85 (70 days) + $55.07 (70 days) = $212.33.
Finally, let's add the interest to the remaining balance: $4,500 + $212.33 = $4,712.33.
Therefore, the final amount due on the loan is $4,712.33. Ringmaster, cue the applause!
To calculate the final amount due on the loan, we need to calculate the interest charge and subtract the partial payments from the original loan amount.
Step 1: Calculate the interest charge after 40 days.
Interest = Principal x Rate x Time
Interest = $8,500 x 0.06 x (40/360)
Interest = $283.33
Step 2: Subtract the first partial payment from the original loan amount.
Remaining Loan = $8,500 - $2,000
Remaining Loan = $6,500
Step 3: Calculate the interest charge after 70 days.
Interest = Remaining Loan x Rate x Time
Interest = $6,500 x 0.06 x (70/360)
Interest = $267.50
Step 4: Subtract the second partial payment from the remaining loan amount.
Remaining Loan = $6,500 - $2,000
Remaining Loan = $4,500
Step 5: Add the previous interest charges to the remaining loan amount.
Total Interest = $283.33 + $267.50
Total Interest = $550.83
Final Amount Due = Remaining Loan + Total Interest
Final Amount Due = $4,500 + $550.83
Final Amount Due = $5,050.83
Therefore, the final amount due on the loan is $5,050.83.
To find the final amount due on the loan, we need to calculate the interest for the entire duration of the loan and subtract the partial payments made by Alicia.
First, let's calculate the interest accrued for the full 180-day loan term. The formula to calculate simple interest is:
Interest = Principal × Rate × Time
The principal is $8,500, the rate is 6% (0.06 as a decimal), and the time is 180 days. Plugging these values into the formula, we get:
Interest = $8,500 × 0.06 × 180/365
We divide by 365 to account for the fact that the interest rate is calculated annually, but the loan term is given in days.
Interest = $255.07 (rounded to two decimal places)
Now, let's subtract the partial payments made by Alicia. After 40 days, she made a payment of $2,000, and after another 70 days, she made a second payment of $2,000. Therefore, the total partial payments made are:
Total Partial Payments = $2,000 + $2,000 = $4,000
Finally, to find the final amount due, we subtract the total partial payments from the original loan amount plus interest:
Final Amount Due = Principal + Interest - Total Partial Payments
= $8,500 + $255.07 - $4,000
= $4,755.07
Therefore, the final amount due on the loan is $4,755.07.