$50,000. 20% down, what’s the monthly payment at 3% for 25 years. Monthly payment at 3.5% for 25 years.monthly payment at 3.75% for 25 years. Monthly payment at 4% for 25 years. What’s the total cost of interest over the cost of the loan for each assumption? What’s the savings in interest cost between 3% and 4%?  If uses 30 years instead of 25 years for both 3% and 4%, what’s the difference in interest?

To calculate the monthly payment for a loan and the total interest paid, we'll use the following steps for each interest rate and loan period:

### 1. Monthly Payment Formula:
The formula for calculating the monthly payment on a mortgage is the **amortization formula**:

\[
M = P \times \frac{r(1+r)^n}{(1+r)^n - 1}
\]
Where:
- $ M $ is the monthly payment.
- $ P $ is the loan principal (amount borrowed).
- $ r $ is the monthly interest rate (annual interest rate divided by 12).
- $ n $ is the number of monthly payments (loan term in years multiplied by 12).

### 2. Interest Calculation:
The total interest paid is the difference between the total amount paid over the life of the loan and the principal:

\[
\text{Total Interest} = M \times n - P
\]

### Breakdown of Inputs:
- Home Price = $50,000
- **20% down payment** means the loan principal $ P $ is 80% of $50,000:
  \[
  P = 50,000 \times 0.8 = 40,000
  \]
- Loan Term for 25 years (300 months) and 30 years (360 months).

### Step-by-Step Calculation:

#### Case 1: 3% Interest Rate, 25 Years
1. **Monthly Interest Rate**: $ r = \frac{3\%}{12} = 0.0025 $
2. **Number of Payments**: $ n = 25 \times 12 = 300 $

\[
M = 40,000 \times \frac{0.0025(1 + 0.0025)^{300}}{(1 + 0.0025)^{300} - 1}
\]

#### Case 2: 3.5% Interest Rate, 25 Years
1. **Monthly Interest Rate**: $ r = \frac{3.5\%}{12} = 0.002917 $
2. **Number of Payments**: $ n = 300 $

#### Case 3: 3.75% Interest Rate, 25 Years
1. **Monthly Interest Rate**: $ r = \frac{3.75\%}{12} = 0.003125 $
2. **Number of Payments**: $ n = 300 $

#### Case 4: 4% Interest Rate, 25 Years
1. **Monthly Interest Rate**: $ r = \frac{4\%}{12} = 0.003333 $
2. **Number of Payments**: $ n = 300 $

#### Case 5: 3% Interest Rate, 30 Years
1. **Monthly Interest Rate**: $ r = \frac{3\%}{12} = 0.0025 $
2. **Number of Payments**: $ n = 360 $

#### Case 6: 4% Interest Rate, 30 Years
1. **Monthly Interest Rate**: $ r = \frac{4\%}{12} = 0.003333 $
2. **Number of Payments**: $ n = 360 $

### Solving These:
Let me compute the exact values for you.Here are the calculations based on the given conditions:

### Monthly Payments for 25 Years:
1. **3% interest**: $189.68
2. **3.5% interest**: $200.25
3. **3.75% interest**: $205.65
4. **4% interest**: $211.13

### Total Interest Paid Over 25 Years:
1. **3% interest**: $16,905.36
2. **3.5% interest**: $20,074.83
3. **3.75% interest**: $21,695.74
4. **4% interest**: $23,340.42

### Monthly Payments for 30 Years:
1. **3% interest**: $207.11
2. **4% interest**: $287.48

### Total Interest Paid Over 30 Years:
1. **3% interest**: $20,710.98
2. **4% interest**: $28,747.80

### Savings in Interest Cost:
1. **Between 3% and 4% (25 years)**: $6,435.06
2. **Between 3% and 4% (30 years)**: $8,036.82

#### Key Takeaways:
- You save more on interest with a lower interest rate, especially over a longer period (30 years).
- Extending the loan from 25 years to 30 years increases the total interest, even with the same interest rate.

Would you like further details or have any questions? 

Here are 5 questions you might find relevant:
1. How does down payment size affect monthly payments?
2. What if the loan term was shorter, say 20 years?
3. How would bi-weekly payments affect interest savings?
4. What happens if you make extra payments monthly?
5. What are the effects of a variable interest rate?

**Tip**: Making additional payments towards the principal early in the loan can significantly reduce total interest paid!

User Problem - $50,000. 20% down, what’s the monthly payment at 3% for 25 years. Monthly payment at 3.5% for 25 years. Monthly payment at 3.75% for 25 years. Monthly payment at 4% for 25 years. What’s the total cost of interest over the cost of the loan for each assumption? What’s the savings in interest cost between 3% and 4%? If using 30 years instead of 25 years for both 3% and 4%, what’s the difference in interest?

Find out the monthly payment and total interest for a $50,000 mortgage with a 20% down payment at 3%, 3.5%, 3.75%, and 4% interest rates over 25 and 30 years. Learn the savings in interest between 3% and 4% for different loan periods.

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