Max Wholesaler borrowed $2,000 on a 10%, 120-day note. After 45 days, Max paid $700 on the note. Thirty days later, Max paid an additional $630. Use ordinary interest.

Determine the total interest using the U.S. Rule.

Note: Round your intermediate balances and interest amounts to the nearest cent. Round your final answer to the nearest cent.

Determine the ending balance due using the U.S. Rule.

Note: Round your intermediate balances and interest amounts to the nearest cent. Round your final answer to the nearest cent.

The U.S. Rule is used to compute interest on loans with partial payments before the due date, applying each payment to accrued interest first, then to the principal. We need to calculate the total interest and the balance due on the 10%, 120-day note for Max Wholesaler.

### Given:
- Principal: $2,000
- Interest rate: 10% (annual rate)
- Time for the loan: 120 days
- First payment: $700 after 45 days
- Second payment: $630 after 75 days (30 days after the first payment)

We will use ordinary interest, which means assuming a year consists of 360 days for calculations. Let’s break the problem into steps.

### Step 1: Calculate interest accrued for the first 45 days
The formula for ordinary interest is:
\[
\text{Interest} = P \times r \times \frac{t}{360}
\]
Where:
- $P$ is the principal,
- $r$ is the annual interest rate (expressed as a decimal),
- $t$ is the time in days.

For the first 45 days:
\[
\text{Interest} = 2000 \times 0.10 \times \frac{45}{360} = 25.00
\]
So, after 45 days, the accrued interest is $25.00.

### Step 2: Apply the first payment ($700)
Since Max paid $700 after 45 days, the interest accrued ($25.00) is deducted first. Then, the remaining amount of the payment is applied to reduce the principal.

\[
\text{Remaining payment} = 700 - 25 = 675
\]
Now, we subtract this from the original principal:
\[
\text{New principal} = 2000 - 675 = 1325
\]

### Step 3: Calculate interest for the next 30 days
Now, we calculate the interest on the new principal ($1,325) for the next 30 days (from day 45 to day 75):
\[
\text{Interest} = 1325 \times 0.10 \times \frac{30}{360} = 11.04
\]

### Step 4: Apply the second payment ($630)
Max made a second payment of $630 after 75 days. Again, we first subtract the accrued interest ($11.04) from the payment:
\[
\text{Remaining payment} = 630 - 11.04 = 618.96
\]
Now, apply this remaining amount to reduce the principal:
\[
\text{New principal} = 1325 - 618.96 = 706.04
\]

### Step 5: Calculate interest for the remaining 45 days
Finally, we calculate the interest on the remaining principal ($706.04) for the last 45 days (from day 75 to day 120):
\[
\text{Interest} = 706.04 \times 0.10 \times \frac{45}{360} = 8.82
\]

### Step 6: Determine the total interest and ending balance
The total interest is the sum of all interest amounts:
\[
\text{Total interest} = 25.00 + 11.04 + 8.82 = 44.86
\]

The ending balance due on the note is the remaining principal plus the final accrued interest:
\[
\text{Ending balance} = 706.04 + 8.82 = 714.86
\]

### Final Results:
- **Total interest:** $44.86
- **Ending balance due:** $714.86

Would you like any more details, or do you have any questions?

### Additional Questions:
1. How would the calculations change if the interest rate was compounded instead of simple?
2. How does the U.S. Rule differ from other interest calculation methods like compound interest?
3. What if Max made only one payment at the end of the 120 days—how would the interest and balance be affected?
4. How would the interest be calculated if Max paid $1,000 in the first payment?
5. How does rounding intermediate steps affect the final interest calculation?

### Tip:
Always double-check your time periods when calculating interest, especially when partial payments are involved. It can be easy to miscount the days, which impacts the final balance!

Max Wholesaler borrowed $2,000 on a 10%, 120-day note. After 45 days, Max paid $700 on the note. Thirty days later, Max paid an additional $630. Use ordinary interest. Determine the total interest using the U.S. Rule. Determine the ending balance due using the U.S. Rule.

Learn how to calculate total interest and the ending balance on a $2,000 loan using the U.S. Rule with ordinary interest. Includes a detailed step-by-step solution for partial payments of $700 after 45 days and $630 after 75 days on a 10%, 120-day loan. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation