Not yet answered Points out of 10.00 p Flag question You have a $$ \$ 22,500 $$ line of credit which charges an annual percentage rate of prime rate plus $$ 5 \% $$. Your starting balance on April 1 was $$ \$ 6,750 $$. On April you made a payment of $$ \$ 2,500 $$. On April 14 you borrowed $$ \$ 5,100 $$, and on April 17 you borrowed $$ \$ 3,800 $$. If the current prime rate is $$ 8 \% $$, what is your ne balance? Select one: a. $$ \$ 15,885.12 $$ b. $$ \$ 13,150.00 $$ c. $$ \$ 13,250.17 $$ d. $$ \$ 14,699.54 $$

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UpStudy AI · Accepted Answer

To find the new balance on the line of credit, we need to follow these steps:

1. **Calculate the annual percentage rate (APR)**:
   - The prime rate is $$ 8\% $$.
   - The APR is $$ 8\% + 5\% = 13\% $$.

2. **Calculate the daily interest rate**:
   - The daily interest rate is calculated by dividing the APR by the number of days in a year (assuming 365 days):
   $$
   \text{Daily Interest Rate} = \frac{13\%}{365} = \frac{0.13}{365}
   $$

3. **Calculate the interest accrued from April 1 to April 30**:
   - The starting balance on April 1 is $$ \$6,750 $$.
   - The payment of $$ \$2,500 $$ is made on April 1.
   - The balance after the payment is:
   $$
   \text{Balance after payment} = 6750 - 2500 = 4250
   $$
   - From April 1 to April 14 (13 days), the interest on $$ \$4,250 $$ is:
   $$
   \text{Interest from April 1 to April 14} = 4250 \times \left(\frac{0.13}{365}\right) \times 13
   $$
   - On April 14, you borrow $$ \$5,100 $$, so the new balance becomes:
   $$
   \text{New Balance after borrowing} = 4250 + 5100 = 9350
   $$
   - From April 14 to April 17 (3 days), the interest on $$ \$9,350 $$ is:
   $$
   \text{Interest from April 14 to April 17} = 9350 \times \left(\frac{0.13}{365}\right) \times 3
   $$
   - On April 17, you borrow $$ \$3,800 $$, so the new balance becomes:
   $$
   \text{New Balance after borrowing} = 9350 + 3800 = 13150
   $$
   - From April 17 to April 30 (13 days), the interest on $$ \$13,150 $$ is:
   $$
   \text{Interest from April 17 to April 30} = 13150 \times \left(\frac{0.13}{365}\right) \times 13
   $$

4. **Calculate the total interest and the final balance**:
   - The total interest accrued over the month will be the sum of the interest calculated in each period.

Now, let's perform the calculations step by step.

### Step 1: Calculate Daily Interest Rate
$$
\text{Daily Interest Rate} = \frac{0.13}{365}
$$

### Step 2: Calculate Interest for Each Period
1. **From April 1 to April 14**:
   $$
   \text{Interest} = 4250 \times \left(\frac{0.13}{365}\right) \times 13
   $$

2. **From April 14 to April 17**:
   $$
   \text{Interest} = 9350 \times \left(\frac{0.13}{365}\right) \times 3
   $$

3. **From April 17 to April 30**:
   $$
   \text{Interest} = 13150 \times \left(\frac{0.13}{365}\right) \times 13
   $$

Now, I will calculate these values.
Calculate the value by following steps:
- step0: Calculate:
  $$13150\left(\frac{0.13}{365}\right)\times 13$$
- step1: Divide the terms:
  $$13150\times \frac{13}{36500}\times 13$$
- step2: Multiply the terms:
  $$\frac{3419}{730}\times 13$$
- step3: Multiply:
  $$\frac{3419\times 13}{730}$$
- step4: Multiply:
  $$\frac{44447}{730}$$
Calculate or simplify the expression $$ 9350 * (0.13 / 365) * 3 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$9350\left(\frac{0.13}{365}\right)\times 3$$
- step1: Divide the terms:
  $$9350\times \frac{13}{36500}\times 3$$
- step2: Multiply the terms:
  $$\frac{2431}{730}\times 3$$
- step3: Multiply:
  $$\frac{2431\times 3}{730}$$
- step4: Multiply:
  $$\frac{7293}{730}$$
Calculate or simplify the expression $$ 4250 * (0.13 / 365) * 13 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$4250\left(\frac{0.13}{365}\right)\times 13$$
- step1: Divide the terms:
  $$4250\times \frac{13}{36500}\times 13$$
- step2: Multiply the terms:
  $$\frac{221}{146}\times 13$$
- step3: Multiply:
  $$\frac{221\times 13}{146}$$
- step4: Multiply:
  $$\frac{2873}{146}$$
Now that we have calculated the interest for each period, let's summarize the results:

1. **Interest from April 1 to April 14**:
   $$
   \text{Interest} \approx 19.68
   $$

2. **Interest from April 14 to April 17**:
   $$
   \text{Interest} \approx 9.99
   $$

3. **Interest from April 17 to April 30**:
   $$
   \text{Interest} \approx 60.89
   $$

### Step 3: Calculate Total Interest
Now, we will sum up the interest accrued over the month:
$$
\text{Total Interest} = 19.68 + 9.99 + 60.89
$$

### Step 4: Calculate Final Balance
The final balance will be the last balance after all transactions plus the total interest:
$$
\text{Final Balance} = 13150 + \text{Total Interest}
$$

Let's calculate the total interest and the final balance.
Calculate the value by following steps:
- step0: Calculate:
  $$19.68+9.99+60.89$$
- step1: Add the numbers:
  $$90.56$$
Calculate or simplify the expression $$ 13150 + 90.56 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$13150+90.56$$
- step1: Add the numbers:
  $$13240.56$$
The total interest accrued over the month is approximately $$ 90.56 $$.

### Final Balance Calculation
Now, adding this interest to the last balance:
$$
\text{Final Balance} = 13150 + 90.56 \approx 13240.56
$$

### Conclusion
The new balance is approximately $$ \$13,240.56 $$.

Since this value does not match any of the provided options exactly, let's check the closest option. The closest option is:

- **c. $$ \$ 13,250.17 $$**

Thus, the answer is **c. $$ \$ 13,250.17 $$**.
The new balance is approximately \$13,250.17.

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