Consider the following loan. Complete parts​ (a)-© below. An individual borrowed ​$76 comma 000 at an APR of 3​%, which will be paid off with monthly payments of ​$360 for 25 years. the amount borrowed is? the annual interest rate is? the number of payments per year is? the loan term is how many years? and the payment is how much?
Answer
Amount borrowed: $76,000; Annual interest rate: 3%; Number of payments per year: 12; Loan term: 25 years; Monthly payment: $360
Explanation
To solve this problem, we need to identify the key components of the loan. The amount borrowed is given as $76,000. The annual percentage rate (APR) is 3%. The number of payments per year is typically 12 for monthly payments. The loan term is specified as 25 years. The monthly payment amount is given as $360
Amount borrowed: $76,000
Annual interest rate: 3%
Number of payments per year: 12
Loan term: 25 years. The percentage paid toward the principal is? and the percentage paid for interest is?

To calculate the percentage of the total payments paid toward the principal and interest, we need to compute the total payments over the life of the loan and separate the interest from the principal.

### Key Values:
- Amount borrowed (Principal): $ P = 76,000 $
- Annual Interest Rate (APR): $ r = 3\% = 0.03 $
- Monthly Interest Rate: $ \frac{0.03}{12} = 0.0025 $
- Loan Term: $ n = 25 \, \text{years} $
- Number of payments per year: $ 12 $
- Monthly Payment: $ M = 360 $

### Step 1: Total Number of Payments
\[
N = n \times 12 = 25 \times 12 = 300
\]

### Step 2: Total Payments Over the Loan Term
\[
\text{Total Payments} = M \times N = 360 \times 300 = 108,000
\]

### Step 3: Total Interest Paid
The total interest paid over the life of the loan is the total payments minus the principal:
\[
\text{Total Interest} = \text{Total Payments} - P = 108,000 - 76,000 = 32,000
\]

### Step 4: Percentages
- **Percentage Paid Toward Principal:**
\[
\text{Percent to Principal} = \left( \frac{\text{Principal}}{\text{Total Payments}} \right) \times 100 = \left( \frac{76,000}{108,000} \right) \times 100 \approx 70.37\%
\]

- **Percentage Paid Toward Interest:**
\[
\text{Percent to Interest} = \left( \frac{\text{Total Interest}}{\text{Total Payments}} \right) \times 100 = \left( \frac{32,000}{108,000} \right) \times 100 \approx 29.63\%
\]

### Final Answer:
- **Percentage Paid Toward Principal:** $ 70.37\% $
- **Percentage Paid Toward Interest:** $ 29.63\% $

### Explanation:
- A significant portion of the payments goes toward the principal, indicating that a smaller fraction of the payments is allocated to interest due to the relatively low interest rate of 3%.

Would you like me to verify these calculations with a detailed amortization schedule or graph?

---

### 5 Follow-Up Questions:
1. What is the formula for calculating monthly loan payments, and how does it relate to the amortization schedule?
2. How does an increase in the loan term affect the total interest paid over the life of the loan?
3. How would a higher interest rate impact the percentage paid toward principal vs. interest?
4. How does making extra payments toward the principal affect the loan balance and interest over time?
5. Could you calculate the interest saved by refinancing to a lower APR, say 2.5%?

### Tip:
When planning to pay off loans faster, prioritize making extra payments toward the principal. This reduces both the total interest and the time required to pay off the loan.

Consider the following loan. Complete parts​ (a)-© below. An individual borrowed ​$76,000 at an APR of 3%, which will be paid off with monthly payments of ​$360 for 25 years. The amount borrowed is? The annual interest rate is? The number of payments per year is? The loan term is how many years? And the payment is how much? Additionally, the percentage paid toward the principal is? And the percentage paid for interest is?

Explore the detailed solution for a $76,000 loan at 3% APR with $360 monthly payments over 25 years. Learn key concepts like loan amortization, total interest, and the percentage paid toward principal and interest. Suitable for high school students and beyond.

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