Andres Michael bought a new boat. He took out a loan for $24,500 at 4.5% interest for 2 years. He made a $4,500 partial payment at 2 months and another partial payment of $3,000 at 6 months. How much is due at maturity?

Note: Do not round intermediate calculations. Round your answer to the nearest cent.

To determine the amount due at maturity, we'll apply the **U.S. Rule**, which adjusts the balance with each partial payment. The U.S. Rule calculates interest only on the unpaid balance at each stage and subtracts the payments accordingly. Here's how we solve the problem step by step:

### 1. Calculate the interest rate per period.
Since the interest rate is annual, and the loan duration is 2 years, we convert the interest rate to a monthly interest rate:

\[
\text{Monthly Interest Rate} = \frac{4.5\%}{12} = 0.00375
\]

### 2. Calculate the initial interest for the first two months.
We begin by calculating how much interest accrues during the first two months (before the first partial payment):

\[
\text{Interest after 2 months} = 24,500 \times 0.00375 \times 2 = 183.75
\]

This gives us the total amount after 2 months (including interest):

\[
\text{Amount after 2 months} = 24,500 + 183.75 = 24,683.75
\]

Now, after 2 months, Andres made a partial payment of $4,500. Subtracting this from the balance:

\[
\text{New balance after 2 months} = 24,683.75 - 4,500 = 20,183.75
\]

### 3. Calculate the interest accrued in the next 4 months.
Next, we calculate the interest on the new balance over the next 4 months (before the second partial payment):

\[
\text{Interest after 4 months} = 20,183.75 \times 0.00375 \times 4 = 302.76
\]

This gives us the total amount after 6 months:

\[
\text{Amount after 6 months} = 20,183.75 + 302.76 = 20,486.51
\]

At this point, Andres made another partial payment of $3,000. Subtracting this from the balance:

\[
\text{New balance after 6 months} = 20,486.51 - 3,000 = 17,486.51
\]

### 4. Calculate the interest accrued for the remaining 18 months.
Now, we calculate the interest on the remaining balance over the next 18 months (until maturity):

\[
\text{Interest for 18 months} = 17,486.51 \times 0.00375 \times 18 = 1,179.94
\]

Adding this interest to the balance gives us the total amount due at maturity:

\[
\text{Amount due at maturity} = 17,486.51 + 1,179.94 = 18,666.45
\]

### Final Answer:
The amount due at maturity is **$18,666.45**.

---

Would you like any further details on these steps?

Here are 5 related questions for further practice:
1. What would the balance be if no partial payments were made until the end of the loan term?
2. How does changing the interest rate affect the total amount due at maturity?
3. What would be the amount due at maturity if the partial payments were made at different intervals (e.g., 3 months and 9 months)?
4. What is the impact of paying a larger first partial payment compared to the second?
5. How is the monthly interest rate calculated from the annual rate?

**Tip:** When solving interest problems, always be careful with rounding; it's best to keep intermediate values unrounded to maintain accuracy.

Andres Michael bought a new boat. He took out a loan for $24,500 at 4.5% interest for 2 years. He made a $4,500 partial payment at 2 months and another partial payment of $3,000 at 6 months. How much is due at maturity?

Learn how to calculate the amount due at maturity for a loan of $24,500 with a 4.5% interest rate over 2 years, considering partial payments made at 2 and 6 months. This detailed step-by-step solution uses the U.S. Rule for interest calculation, making it suitable for students in Grades 10-12.

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