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?
interest for first 40 days = 8500(40/365)(.06)
= $55.89
total owing at that time =$ 8555.89
makes payment of $2000
Balance remaining = 6555.89
interest for next 70 days = 6555.89(70/365)(.06)
= 75.44
total owing at that time = 6631.33
makes payment of $2000, leaving a balance of
4631.33
interest for remaining 70 days
= 4631.33(70/365)(.06) = 53.29
for a balance remaining of $ 4684.62
check my arithmetic, did not write it down on paper first.
To find the final amount due on the loan, we need to calculate the remaining balance after the partial payments and include the interest for the entire loan term.
Step 1: Calculate the remaining balance after the first partial payment.
To do this, subtract the first partial payment of $2,000 from the original loan amount of $8,500:
$8,500 - $2,000 = $6,500
Step 2: Calculate the remaining balance after the second partial payment.
After another 70 days, Alicia made a second partial payment of $2,000. To find the remaining balance, subtract this payment from the previous balance:
$6,500 - $2,000 = $4,500
Step 3: Calculate the interest accrued for the entire loan term.
To find the interest accrued, we need to calculate the interest for the full 180-day term.
First, calculate the interest per day:
Interest per day = Principal * Interest Rate * Time
= $4,500 * 0.06 * (180/365)
= $13.97 (rounded to two decimal places)
Next, calculate the interest accrued for the entire loan term:
Total interest = Interest per day * Total days
= $13.97 * 180 days
= $2,515.40 (rounded to two decimal places)
Step 4: Add the remaining balance and the interest accrued:
Final amount due = Remaining balance + Total interest
= $4,500 + $2,515.40
= $7,015.40 (rounded to two decimal places)
Therefore, the final amount due on the loan is $7,015.40.