Central Auto Parts borrowed $$ \$ 250,000 $$ at $$ 9 \% $$ interest on July 12 for 140 days. (a) If the bank uses the ordinary interest method, what is the amount (in $$ \$ $$ ) of interest on the loan? $$ \$ 8,750 $$ (b) What is the maturity date? December $$ \checkmark imes $$ Need Help? Read it SUBMIT ANSWER

Question

Central Auto Parts borrowed $$ \$ 250,000 $$ at $$ 9 \% $$ interest on July 12 for 140 days. (a) If the bank uses the ordinary interest method, what is the amount (in $$ \$ $$ ) of interest on the loan? $$ \$ 8,750 $$ (b) What is the maturity date? December $$ \checkmark 	imes $$ Need Help? Read it SUBMIT ANSWER

UpStudy AI · Accepted Answer

To solve the problem, we will follow these steps:

### Part (a): Calculate the Interest Using the Ordinary Interest Method

1. **Identify the known values:**
   - Principal amount ($$ P $$): $$ 250,000 $$
   - Interest rate ($$ r $$): $$ 9\% = 0.09 $$
   - Time ($$ t $$): $$ 140 $$ days

2. **Ordinary interest method:**
   - The ordinary interest method uses a 360-day year for calculations.
   - The formula for calculating interest is:
     $$
     I = P \times r \times \frac{t}{360}
     $$

3. **Substituting the values into the formula:**
   $$
   I = 250,000 \times 0.09 \times \frac{140}{360}
   $$

4. **Calculating the interest:**
   - First, calculate $$ \frac{140}{360} $$:
     $$
     \frac{140}{360} = \frac{7}{18} \approx 0.3889
     $$
   - Now, substitute this back into the interest formula:
     $$
     I = 250,000 \times 0.09 \times 0.3889
     $$

5. **Final calculation:**
   $$
   I = 250,000 \times 0.09 \times 0.3889 \approx 8,750
   $$

Thus, the amount of interest on the loan is $$ \$ 8,750 $$.

### Part (b): Calculate the Maturity Date

1. **Identify the loan start date:**
   - Loan start date: July 12

2. **Add the loan duration (140 days) to the start date:**
   - July has $$ 31 $$ days, so from July 12 to July 31 is $$ 19 $$ days.
   - Remaining days to account for: $$ 140 - 19 = 121 $$ days.

3. **Count the days in the following months:**
   - August has $$ 31 $$ days: $$ 121 - 31 = 90 $$ days remaining.
   - September has $$ 30 $$ days: $$ 90 - 30 = 60 $$ days remaining.
   - October has $$ 31 $$ days: $$ 60 - 31 = 29 $$ days remaining.
   - November has $$ 30 $$ days: $$ 29 - 30 = -1 $$ days remaining.

Since we have $$ -1 $$ days remaining after November, the maturity date will be December 1.

### Summary of Answers:
(a) The amount of interest on the loan is $$ \$ 8,750 $$.  
(b) The maturity date is December 1.
(a) The interest on the loan is \$8,750. (b) The maturity date is December 1.

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