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Sagot :
To determine the final amount due on the loan, we'll calculate the interest due and the remaining principal after each partial payment, taking into account the timing of each payment.
Step-by-Step Solution:
Calculate the interest due after 40 days:
Given:
Principal amount (P) = $14,000
Interest rate (r) = 7% per annum (ordinary interest)
Time (t) = 40/365 years (since 40 days out of a 365-day year)
First, calculate the interest for 40 days:
Interest
40
days
=
×
×
Interest
40 days
=P×r×t
Interest
40
days
=
14000
×
0.07
×
40
365
Interest
40 days
=14000×0.07×
365
40
Interest
40
days
≈
135.34
dollars
Interest
40 days
≈135.34 dollars
Calculate the remaining principal after the first partial payment:
After 40 days, you make a partial payment of $1,500.
Remaining principal
=
14000
−
1500
=
12500
dollars
Remaining principal=14000−1500=12500 dollars
Calculate the interest due after another 60 days (total 100 days):
Now, time (t) = 100/365 years.
Calculate the interest for the period from day 41 to day 100:
Interest
60
days
=
Remaining principal
×
×
60
365
Interest
60 days
=Remaining principal×r×
365
60
Interest
60
days
=
12500
×
0.07
×
60
365
Interest
60 days
=12500×0.07×
365
60
Interest
60
days
≈
153.15
dollars
Interest
60 days
≈153.15 dollars
Calculate the remaining principal after the second partial payment:
After 100 days, you make a second partial payment of $2,000.
Remaining principal
=
12500
−
2000
=
10500
dollars
Remaining principal=12500−2000=10500 dollars
Calculate the total interest accrued:
Total interest accrued:
Total interest
=
Interest
40
days
+
Interest
60
days
Total interest=Interest
40 days
+Interest
60 days
Total interest
≈
135.34
+
153.15
=
288.49
dollars
Total interest≈135.34+153.15=288.49 dollars
Calculate the final amount due on the loan:
Final amount due:
Final amount
=
Remaining principal
+
Total interest
Final amount=Remaining principal+Total interest
Final amount
=
10500
+
288.49
Final amount=10500+288.49
Final amount
≈
10788.49
dollars
Final amount≈10788.49 dollars
Therefore, the final amount due on the loan, rounded to the nearest cent, is approximately $10,788.49.
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