Suppose you take out a loan for 160 days in the amount of $14,000 at 7% ordinary interest. After 40 days, you make a partial payment of $1,500. After another 60 days, you make a second partial payment of $2,000. What is the final amount (in $) due on the loan? (Round your answer to the nearest cent.)



Answer :

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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