7. [0.33/1 Points] DETAILS MRECMBC9 10.1 .044 . 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 $$ \vee imes 1 $$ Need Help? Read it

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7. [0.33/1 Points] DETAILS MRECMBC9 10.1 .044 . 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 $$ \vee 	imes 1 $$ Need Help? Read it

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 period ($$ t $$): $$ 140 $$ days

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

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

Now, let's calculate the interest.

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

1. **Start date:** July 12
2. **Add the loan duration:** 140 days

To find the maturity date, we will add 140 days to July 12.

Now, let's perform the calculations for both parts.

### Calculating Interest and Maturity Date

I'll calculate the interest and determine the maturity date.
Calculate the value by following steps:
- step0: Calculate:
  $$250000\times 0.09\left(\frac{140}{360}\right)$$
- step1: Reduce the fraction:
  $$250000\times 0.09\times \frac{7}{18}$$
- step2: Multiply the terms:
  $$22500\times \frac{7}{18}$$
- step3: Reduce the numbers:
  $$1250\times 7$$
- step4: Multiply the numbers:
  $$8750$$
Calculate or simplify the expression $$ July 12 + 140 days $$.
Simplify the expression by following steps:
- step0: Solution:
  $$July\times 12+140days$$
- step1: Reorder the terms:
  $$12July+140days$$
### Part (a): Interest Calculation

The amount of interest on the loan using the ordinary interest method is:
$$
I = 8750
$$
So, the interest is **\$8,750**.

### Part (b): Maturity Date Calculation

To find the maturity date, we add 140 days to July 12.

- Starting from July 12:
  - July has 31 days, so from July 12 to July 31 is $$ 31 - 12 = 19 $$ days.
  - This leaves $$ 140 - 19 = 121 $$ days to account for in the following months.

- August has 31 days, so after August, we have:
  - $$ 121 - 31 = 90 $$ days remaining.

- September has 30 days, so after September, we have:
  - $$ 90 - 30 = 60 $$ days remaining.

- October has 31 days, so after October, we have:
  - $$ 60 - 31 = 29 $$ days remaining.

- Finally, we move into November, where we add the remaining 29 days:
  - Starting from November 1, adding 29 days brings us to November 30.

Thus, the maturity date is **November 30**.

### Summary of Answers:
(a) The amount of interest is **\$8,750**.  
(b) The maturity date is **November 30**.
(a) The interest on the loan is \$8,750. (b) The maturity date is November 30.

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